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Resources tagged with: Place value

There are 133 NRICH Mathematical resources connected to Place value , you may find related items under Place value and the number system .

The Number Jumbler

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Digit Addition

Try out this number trick. What happens with different starting numbers? What do you notice?

Dicey Operations in Line

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Dicey Addition

Who said that adding couldn't be fun?

Where should you start, if you want to finish back where you started?

Forwards Add Backwards

What happens when you add a three digit number to its reverse?

By selecting digits for an addition grid, what targets can you make?

Subtraction Surprise

Try out some calculations. Are you surprised by the results?

Multiply Multiples 3

Have a go at balancing this equation. Can you find different ways of doing it?

Round the Dice Decimals 1

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Round the Three Dice

What happens when you round these three-digit numbers to the nearest 100?

Round the Dice Decimals 2

What happens when you round these numbers to the nearest whole number?

Multiply Multiples 2

Can you work out some different ways to balance this equation?

Multiply Multiples 1

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Two Spinners

What two-digit numbers can you make with these two dice? What can't you make?

Snail One Hundred

In this game, you throw a dice and move counters along the snail's body and in a spiral around the snail's shell. It is about understanding tens and ones.

That Number Square

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

Always a Multiple?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Light the Lights

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Our Numbers

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

Dicey Operations

Nice or Nasty

There are nasty versions of this dice game but we'll start with the nice ones...

Coded Hundred Square

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Two-digit Targets

You have a set of the digits from 0 to 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

Four-digit Targets

You have two sets of the digits 0-9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

What Do You Need?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Method in Multiplying Madness?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

Diagonal Sums

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

An Easy Way to Multiply by 10?

Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?

How Many Miles to Go?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

What an Odd Fact(or)

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

The Deca Tree

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Can you replace the letters with numbers? Is there only one solution in each case?

Sixty-seven Squared

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?

Six Times Five

How many six digit numbers are there which DO NOT contain a 5?

Which Is Quicker?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Think of Two Numbers

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

All the Digits

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Number Rules - OK

Can you produce convincing arguments that a selection of statements about numbers are true?

Two and Two

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Which Scripts?

There are six numbers written in five different scripts. Can you sort out which is which?

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Legs Eleven

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

2-digit Square

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Latin Numbers

Can you create a Latin Square from multiples of a six digit number?

Number Detective

Follow the clues to find the mystery number.

Writing Digits

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

If you put three beads onto a tens/ones abacus you can make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

Place Value

September 3, 2022.

Scheme of work: Key Stage 3: Year 7: Term 1: Place Value

Prerequisite Knowledge

• Find 1000 more or less than a given number.
• Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
• Order and compare numbers beyond 1000
• Identify, represent and estimate numbers using different representations
• Round any number to the nearest 10, 100 or 1000
• Solve number and practical problems involving the above and increasingly large positive numbers.
• Read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include zero and place value.

Key Concepts

• The ability to arrange digits in a place value table is crucial to accessing future topics such as fractions, percentages and many more.
• When multiplying and dividing by 10, 100 and 1000, students can benefit from visualising the digit shift between columns in the place value table.
• To interpret a number scale, students need to have a secure understanding of using the place value table.
• Students often confuse the direction of the inequality symbols when comparing numbers.

Working Mathematically

• Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals.
• Reason mathematically
• Extend their understanding of the number system; make connections between number relationships,
• Solve problems
• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Subject Content

• understand and use place value for decimals, measures and integers of any size
• order positive and negative integers, decimals and fractions; use the number line as a model for ordering the real numbers; use the symbols =, > and <
• use the four operations, including formal written methods, to integers and decimals.

Place Value Resources

Video Tutorial (Free for all)

Online Lesson (Lite/Full)

Downloadable Resources (Full)

Extended Learning

Problem Solving

Mr Mathematics Blog

Planes of symmetry in 3d shapes.

Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.

Regions in the Complex Plane

Explore Regions in the Complex Plane with A-Level Further Maths: inequalities, Argand diagrams, and geometric interpretations.

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Place Value – Definition with Examples

Created: January 3, 2024

Last updated: January 10, 2024

Place Value is an essential and fundamental concept in mathematics that enables us to comprehend and work effectively with numbers. At Brighterly , we understand the importance of mastering place value for building a strong foundation in mathematics, as it plays a critical role in arithmetic operations, problem-solving, and overall number sense. In this comprehensive article, we will delve deep into place value, unraveling its various aspects and significance.

What is Place Value?

Place value is the system of attributing a value to a digit in a number depending on its position. It is a crucial concept that facilitates our ability to read, write, and comprehend numbers, making calculations more straightforward and efficient. Place value ensures that each digit in a number contributes differently based on its position. For instance, consider the number 7,548. The place value of 7 is 7,000, as it is in the thousands place; the place value of 5 is 500, as it is in the hundreds place; the place value of 4 is 40, as it is in the tens place; and finally, the place value of 8 is 8, as it is in the ones place.

Understanding place value is the cornerstone of the base-10 numeral system, which is the most commonly used number system worldwide. By learning place value, children develop a strong foundation in mathematics, enabling them to tackle more complex topics with ease. At Brighterly, we focus on teaching place value concepts in a fun and engaging manner, ensuring that children develop a clear understanding and appreciation of the importance of place value in their mathematical journey.

Place Value Worksheet PDF

Place Value Worksheet

Place Value Worksheets Free PDF

Place Value Worksheets Free

Don’t forget to use math worksheets for kids available on the Brighterly to further enhance your skills!

Place Value Chart

A place value chart is a visual representation of the positions of digits in a number. It helps us understand the value of each digit and makes it easy to compare and manipulate numbers. A typical place value chart consists of columns for units, tens, hundreds, thousands, and so on.

Place Value Meaning

The meaning of place value is the value assigned to each digit based on its position within a number. As we move from right to left, each position represents a power of 10. For example, in the number 7,651, the place value of 7 is 7,000 (7 * 10^3), the place value of 6 is 600 (6 * 10^2), the place value of 5 is 50 (5 * 10^1), and the place value of 1 is 1 (1 * 10^0). This system is essential for understanding how numbers work and for performing calculations.

Comparison Between Indian and International System

The Indian and International systems of place value differ in the way they group digits. In the Indian system, digits are grouped in pairs after the hundredth place, whereas in the International system, digits are grouped in threes. For example, the number 5,678,901 is written as 56,78,901 in the Indian system and as 5,678,901 in the International system. This difference affects the naming of larger numbers and the way they are read aloud. You can learn more about the Indian and International systems of place value by visiting this link.

Place Value for Decimals

Place value for decimals works similarly to whole numbers but extends to the right of the decimal point. Each position to the right of the decimal point represents a negative power of 10. For example, in the number 0.123, the place value of 1 is 1/10 (1 * 10^(-1)), the place value of 2 is 2/100 (2 * 10^(-2)), and the place value of 3 is 3/1000 (3 * 10^(-3)). Understanding place value for decimals is crucial for working with fractions, measurements, and other real-world quantities.

Place Value in Numbers

Place value in numbers is the cornerstone of the base-10 numeral system, which is the most commonly used number system worldwide. Understanding place value in numbers allows us to represent and manipulate numbers efficiently. For example, when we add or subtract numbers, we align them according to their place values and perform operations on corresponding digits.

Face Value in Maths

Face value is the value of a digit itself, irrespective of its position in a number. In other words, the face value of a digit is the same no matter where it appears in a number. For example, the face value of 5 in the numbers 5, 25, 354, and 5,807 is always 5.

Difference Between Place Value and Face Value

The main difference between place value and face value is that place value depends on the position of a digit within a number, while face value is the value of a digit itself, independent of its position. Place value helps us understand the overall value of a number and perform arithmetic operations, while face value is a more basic concept that shows the value of individual digits.

Solved Examples on Place Value

To better understand place value, let’s look at some solved examples:

Find the place value of 7 in the number 4,783.

In this number, 7 is in the hundreds place. So, the place value of 7 is 7 * 10^2 = 700.

Determine the place value of 2 in the number 0.023.

In this number, 2 is in the hundredths place. So, the place value of 2 is 2 * 10^(-2) = 2/100 = 0.02.

Free Printable Place Value Worksheets

Place Value Worksheets With Answers

Practice Problems on Place Value

Try solving these practice problems to test your understanding of place value:

• Find the place value of 3 in the number 3,762.
• Determine the place value of 4 in the number 0.049.
• Calculate the place value of 6 in the number 16,205.

Place value is an indispensable concept in mathematics that forms the foundation for understanding and working with numbers effectively. By mastering the intricacies of place value, students can perform arithmetic operations more efficiently, read and write numbers accurately, and develop a robust sense of number sense. At Brighterly, we emphasize the importance of place value in our curriculum, ensuring that children build a strong mathematical foundation from the very beginning.

Through our innovative teaching methods, interactive activities, and engaging content, Brighterly strives to make learning place value an enjoyable and memorable experience for our young learners. We believe that by fostering a deeper understanding of place value, we are empowering students to conquer more complex mathematical concepts with ease and confidence.

As students progress through their mathematical journey, the significance of place value becomes increasingly apparent. From basic arithmetic operations to advanced problem-solving, place value remains a vital tool that bolsters mathematical comprehension and critical thinking. It is our mission at Brighterly to equip children with the knowledge and skills necessary to navigate the fascinating world of mathematics, starting with the mastery of place value.

Frequently Asked Questions on Place Value

What is the place value of 0 in a number.

The place value of 0 in a number is always 0, no matter its position. Zero serves as a placeholder, indicating that there are no units, tens, hundreds, etc., in that position.

Why is place value important?

Place value is important because it allows us to represent and manipulate numbers efficiently. It also forms the basis for arithmetic operations, problem-solving, and overall number sense.

How is place value used in everyday life?

Place value is used in everyday life when we read and write numbers, count, measure, and perform calculations. It helps us understand the value of digits in different positions and makes it easier to perform operations like addition, subtraction, multiplication, and division.

How can I teach place value to children?

Teaching place value to children can be done through various methods, such as using base-10 blocks, place value charts, manipulatives, and real-life examples. Engaging activities and games can also help children develop a strong understanding of place value concepts.

What is the difference between place value and expanded form?

Place value refers to the value of a digit based on its position in a number, while expanded form is a way of writing a number by breaking it down into its individual place values. For example, in the number 543, the place value of 5 is 500, the place value of 4 is 40, and the place value of 3 is 3. The expanded form of this number is 500 + 40 + 3.

• Place Value Concepts – National Council of Teachers of Mathematics
• Place Value – BBC Bitesize
• Understanding Place Value – National Center on Improving Mathematics Instruction

I am a seasoned math tutor with over seven years of experience in the field. Holding a Master’s Degree in Education, I take great joy in nurturing young math enthusiasts, regardless of their age, grade, and skill level. Beyond teaching, I am passionate about spending time with my family, reading, and watching movies. My background also includes knowledge in child psychology, which aids in delivering personalized and effective teaching strategies.

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The number 2600 is expressed in words as “two thousand six hundred”. It comes after two thousand five hundred ninety-nine. For example, if there are two thousand six hundred apples, you have two thousand five hundred ninety-nine apples and then one more. Thousands Hundreds Tens Ones 2 6 0 0 How to Write 2600 in […]

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Place Value Worksheets

And base 10 blocks.

Our place value worksheets focus on deepening a student's understanding of our base 10 system. In our " base 10 blocks " worksheets, students manipulate blocks (units of 1) and rods (groups of 10) to build, deconstruct or add numbers. Later worksheets focus on building or de-constructing multi-digit numbers.

Choose your grade / topic:

Grade 1: Base 10 blocks worksheets

Grade 1: Place value worksheets

Grade 2: Place value worksheets

Grade 3: Place value worksheets

Grade 4: Place value worksheets

Grade 5: Place value worksheets

Topics include:

Grade 1 base 10 blocks worksheets

• Counting and making 10 with ten frames
• Regrouping unit blocks into blocks of 10 ("rods")
• Counting "tens" and "ones"
• Breaking a number (11-99) into rods ("tens") and  blocks ("ones")
• Adding 2 digit numbers with base 10 blocks

Grade 1 place value worksheets

• Identifying tens and ones from 2 digit numbers
• Combining tens and ones into 2 digit numbers
• Identifying a digit's place value (tens, ones)
• Building a 2 digit number with missing addends
• Write 2 digit numbers in expanded form
• Write 2 digit numbers in normal form

Grade 2 place value worksheets

• Building a 3-digit number from the parts
• Missing place values in 3-digit numbers
• Write 3-digit numbers in expanded form
• Write 3-digit numbers in normal form
• Hundreds, tens & ones - identify the underlined digit
• Comparing and ordering numbers up to 100 and 1,000

Grade 3 place value worksheets

• Building 3, 4 and 5-digit numbers from the parts
• Missing place values in 3 and 4-digit numbers
• Write 4-digit numbers in expanded form
• Write 4-digit numbers in expanded notation
• Write 4-digit numbers in standard form
• Identify the place value of the underlined digit
• Compare and order numbers up to 10,000 and 100,000

Grade 4 place value worksheets

• Building 4, 5 and 6-digit numbers from the parts
• Missing place values in 4, 5 and 6-digit numbers
• Write 5-digit numbers in expanded form
• Write 5 digit numbers in expanded notation
• Write 5-digit numbers in standard form

Grade 5 place value worksheets

• Building 5 and 6-digit numbers from the parts
• Missing place values in 5 and 6-digit numbers
• Build numbers from parts with decimals
• Decimal numbers in expanded form
• Decimal numbers in expanded notation

Related topics

Comparing numbers worksheets

Rounding worksheets

Sample Place Value Worksheet

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Place Value Worksheets Hub Page

Welcome to our Place Value Worksheets area.

Here you will find a wide range of place value activites and worksheets which will help your child gain a better understanding of how our number system and place value works.

You can also take a look at our printable place value charts or our place value sheets with decimals or BIG numbers over a million!

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• This page contains links to other Math webpages where you will find a range of activities and resources.
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Place Value Worksheets and Resources

On this page you will find link to our range of place value resources, including online practice, charts and worksheets.

Quicklinks to Place Value ...

• Online Place Value Practice
• Place Value Charts and Number Grids
• Place Value Tens and Ones

Place Value up to Hundreds

Place value up to thousands.

• Big Number Place Value
• Negative Number Place Value
• Decimal Place Value
• Randomly Generated Place Vaue Worksheets

Scientific Notation Support

• Absolute Value Worksheets

Definition of Place Value

So what exactly is place value?

Place value refers to the value of the digits in any given number. In the number 482 for example, the value of the digit '8' is 80 and the value of the digit '4' is 400.

At a more advanced level, in the number 36.57, the value of the digit '5' is 0.5 and the value of the digit '7' is 0.07.

In our number system, each time you move a place to the right, the value of the digit gets ten times bigger. Each time you move a place to the left, the value of the digit gets ten times smaller.

• Definition of Place Value Sheet
• PDF version

Place Value Learning

Children start their learning journey in Math when they start to count. When they are confindent counting small groups of objects and getting beyond 10, they then begin to develop their understanding of place value up to 100 and beyond.

When they have understood how place value with whole numbers works, they can start learning about place value with decimals.

Our selection of free math place value worksheets has been split into different areas below so that you can more easily find the right sheet for your child.

Online Place Value Practice Zone

In our Math Place Value Practice area, you can practice your place value skills, adding thousands, hundreds, tens and ones. You can even use this area for adding on decimals: tenths and hundredths.

You can select the numbers you want to practice with, and print out your results when you have finished.

You can also use the practice zone for benchmarking your performance, or using it with a group of children to gauge progress.

• Free Place Value Practice Zone 1 - Digit Values
• Math Place Value Practice Zone 2 - Combining

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Place Value Charts & Number Grids

Place value charts.

We have a selection of place value charts which are great for helping to develop understanding of place value.

The charts cover a range of numbers from billions to millionths.

They are a good supporting resource for children who are finding place value difficult.

We also have place value grids to help children convert to and from expanded form to support place value learning.

They are also a good way to get children to become familiar with how the number system works.

• Place Value Charts (whole numbers)
• Decimal Place Value Charts
• Place Value Grids

Number Grids

These printable grids will help your child learn to read and write numbers and learn the number sequence.

Some of the charts are partially filled to help your child learn their place value.

Using these sheets will help your child to:

• learn to count in tens and ones;
• learn to read and write numbers.

1st Grade Place Value Charts

• Free Number Chart 1-30
• Number Chart to 50
• Printable Number Charts 0-99
• Hundred Number Charts (100 Squares)
• Missing Number Chart 1-100
• Number Grid up to 200
• Number Grid up to 300

Place Value Games

Here you will find our selection of place value games.

We have a range of different games for helping to teach place value from 2-digit games up to decimal place value games.

There are a range of games are suitable for all ages, from kindergarten and upwards.

• Games to teach Place Value

Place Value and Number Sense Tens and Ones

Here you will find our selection of 2 digit Place Value worksheets.

Using these Math Worksheets Place Value will help your child to:

• learn their place value to 100;
• understand the value of each digit in a 2 digit number;
• Round numbers up to 100 to the nearest 10
• learn to read and write numbers to 100.
• Place Value Worksheets for Kindergarten
• Place Value to 20 Worksheets
• Place Value Ones and Tens Models
• Place Value Tens and Ones (standard and expanded form)
• Basic Math Worksheets - Ordering numbers 2 Digits
• Rounding to the nearest 10 Worksheets
• Add and Subtract 10 Worksheets

Here you will find our selection of 3 digit Place Value worksheets.

• learn their place value with 3 digit numbers;
• understand the value of each digit in a 3 digit number;
• learn to read and write numbers up to 999.
• 2nd Grade Place Value Models up to hundreds
• Second Grade Place Value Worksheets 3 Digits
• Ordering numbers worksheets up to 999

Here you will find our selection of Place Value up to 4 Digits worksheets.

Using these sheets will help your child learn to:

• learn their place value with 4 digit numbers;
• use place value models to understand how to combine thousands, hundreds, tens and ones;
• understand the value of each digit in a 4 digit number;
• learn to use standard and expanded form with 4 digit numbers.
• Place Value Models 4 Digits
• Place Value 4 Digit Numbers Worksheets (conversion)
• Ordering Numbers up to Thousands Sheets

Place Value BIG Numbers

Welcome to our BIG Number Place Value area.

Here you will find sheets to help your child learn their place value to 10 million.

• Know how to read and write numbers to 10 million;
• Understand place value to 10 million.
• Solve place value problems.

All the 4th grade math worksheets in this section support elementary math benchmarks.

• 4th Grade Place Value up to 6 digits
• 5th Grade Place Value Worksheets to 10 million
• 5th Grade Ordering Large Numbers up to 100 million

Place Value Negative Numbers

• learn to order negative numbers;
• learn to position numbers from -10 to 10 on a number line.
• ordering and comparing rational numbers
• Ordering Negative Numbers -10 to 10
• Ordering and Comparing Rational Numbers

Place Value Decimals

Here you will find our selection of Place Value involving Decimals with up to 2 decimal places (2dp).

• learn their place value with decimals up to 2dp;
• understand the value of each digit in a decimal number;
• learn to read and write numbers with up to 2dp.
• Decimal Place Value Worksheets to 2dp
• Place Value to 3dp
• Ordering Decimals Worksheets

Rounding Numbers Worsheets

As well as our random number worksheet generator, we have a wide range of graded rounding worsheets.

These sheets are great for supporting less able students, or for giving an extra challenge to more able students.

Using the link below will take you to our Rounding numbers hub page where you will find links to all our rounding numbers worksheets.

• Rounding Numbers Hub page

Place Value Random Worksheet Generator

Here is our generator for generating your own place value worksheets.

Our generator will create the following worksheets:

• digit values
• comparing numbers
• converting between standard and expanded form

These sheets involve saying the value of the underlined digit.

• Digit Place Value Worksheets
• Standard Form to Expanded Form Worksheets
• Expanded Form to Standard Form Worksheets
• Rounding Off Numbers Worksheets
• Greater Than Less Than Worksheets

We have a selection of worksheets designed to help students learn about asbolute value.

Topics covered include:

• absolute value and opposite numbers
• comparing absolute values
• absolute value arithmetic
• solving absolute value equations

Our Convert to scientific notation calculator will take a number and convert it to scientific notation and e-notation.

It shows you all the working out along the way too.

• Convert to Scientific Notation Calculator
• Standard Notation to Scientific Notation Support page
• Scientific Notation to Standard Notation support page

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Place value

Here you will learn about place value , including the names and values of the different positions.

Students will first learn about place value as part of their work with numbers and operations in base ten in elementary school.

What is place value?

Place value is the value of each digit within a number.

A number is made up of digits. For example, the number 54 has two digits, 5 and 4. The value of each digit can help us understand the size of the number.

To determine the value of a digit within a number you use a place value chart.

For example, for 54, the 5 is in the tens column and the 4 is in the ones column.

This means that the number 54 is equivalent to 5 tens and 4 ones.

5 tens is the same as 5\times{10}=50 and 4 ones is the same as 4\times{1}=4.

Adding 50+4 gives us the number 54.

Whole number place value

Here are the digits to the left of the decimal point.

Let’s write the number nine million, four hundred and fifty thousand, three hundred and eighty two in the place value chart:

Notice you use a comma after the millions digit (9) and the thousands digit (0).

The comma is used to the left of the decimal point to separate 3 digits at a time.

If the value within a column is 0, you must write a zero for that place value. Here, if you missed the 0 in the thousands position, the number would read 945,382 which is a different number from the number above.

The place value chart above shows positions up to the millions. However, you can use place value to represent very large numbers.

Decimal place value

Here are the digits to the right of the decimal point .

Let’s write the number two and thirty four thousandths in the place value chart:

There is a period after the ones digit (2). The period tells us that the next part of the number is a decimal or less than 1.

If the value within a column is 0, you must write a zero for that place value. Here, if you missed the 0 in the tenths position, the number would read 2.34 which is a different number from the number above.

The place value chart above shows numbers down to the thousandths. However, you can use place value to represent very small numbers.

Common Core State Standards

How does this relate to 2nd grade math, 4th grade math and 5th grade math?

• Grade 2 – Numbers and Operations in Base 10 (2.NBT.A.3) Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
• Grade 4 – Numbers and Operations in Base 10 (4.NBT.A.2) Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.
• Grade 5 – Numbers and Operations in Base 10 (5.NBT.A.3) Read, write, and compare decimals to thousandths.

How to write the value of a digit in a number

In order to write the value of a digit in a number:

Find the digit within the number.

Use the place value chart to find the position.

Write the value of the digit.

[FREE] Rounding Numbers Check for Understanding (Grade 3 to 5)

Use this quiz to check your grade 3 to 5 students’ understanding of rounding numbers. 10+ questions with answers covering a range of 3rd, 4th, and 5th grade rounding numbers topics to identify areas of strength and support!

Place value examples

Example 1: whole number place value.

What is the value of the digit 3 in 4,163?

• Find the digit within the number.  

2 Use the place value chart to find the position.

The 3 is in the ones column.

3 Write the value of the digit.

The value of the digit 3 in the number 4,163 is 3 ones, or 3.

Example 2: whole number place value

What is the value of the digit 4 in 385,431?

The 4 is in the hundreds column.

The value of the digit 4 in the number 385,431 is four hundreds, or 400.

Example 3: whole number place value

What is the value of the digit 2 in 1,025,634?

The 2 is in the ten thousands column.

The value of the digit 2 in the number 1,025,634 is twenty thousands, or 20,000.

Example 4: decimal place value

What is the value of the digit 2 in 3.264?

The 2 is in the tenths column.

The value of the digit 2 in the number 3.264 is two tenths, or 0.2.

Example 5: decimal place value

What is the value of the digit 7 in 0.078?

Recall the place value of that column.

The 7 is in the hundredths column.

The value of the digit 7 in the number 0.078 is seven hundredths, or 0.07.

Example 6: decimal place value

What is the value of the digit 4 in 10.054?

Locate the digit within the number.

The 4 is in the thousandths column.

The value of the digit 4 in the number 10.054 is four thousandths, or 0.004.

Teaching tips for place value

• When teaching place value, base ten blocks and other manipulatives can be used to help students visualize place value and see how each position relates to the others.
• Place value is based on patterns in our number system, which many students will pick up on. Asking questions like “What do you notice about these numbers?” or “How does the value of a number change if you change the place value of the digits?” can encourage students to think more broadly about the underlying structure of our place value system.
• Regularly exposing students to place value ideas helps them develop a deeper understanding of our number system. Instead of just using worksheets, incorporate it into math each day with a place value game. Something as simple as “I am thinking of a number that has more than 4 hundreds, what could it be?” can help students remember and think flexibly about place value.
• Reinforce the connection between standard form, expanded form and word form by asking students to provide all three for any given number.

Easy mistakes to make

• Including too many digits All of the digits after a place value position are sometimes wrongly included. For example, What is the value of 4 in the number 243? \quad 43 {\color{red}✘} \quad 40 {\color{green}✔}
• Including a oneths column The first column to the right of the decimal point is the tenths column – there is no oneths column. For example, What is the value of the digit 2 in the number 3.524? \hspace{0.5cm} Two tenths or 0.02 {\color{red}✘} \hspace{3cm} Two hundredths, or 0.02 {\color{green}✔} (Thinking that the first decimal \hspace{1.7cm} (The first decimal position is tenths position is oneths and the second \hspace{1.7cm} and the second is hundredths) is tenths)

Related rounding numbers lessons

• Rounding numbers
• Rounding decimals
• Significant figures

Practice place value questions

1. What is the value of 2 in 475,321?

Two hundreds

The digit 2 is in the tens column, so the value is 2 tens or 20.

2. What is the value of 1 in 1,000,253?

One hundred thousand

The digit 1 is in the millions column, so the value is 1 million or 1,000,000.

3. What is the value of 3 in 483,201?

Ten thousand

The digit 3 is in the thousands column, so the value is 3 thousands or 3,000.

4. What is the value of 7 in 6.072?

Seven hundreds

Seven tenths

Seven hundredths

The digit 7 is in the hundredths column, so the value is 7 hundredths or 0.07.

5. What is the value of 8 in 0.008?

Eight thousandths

Eight tenths

Eight thousands

The digit 8 is in the thousandths column, so the value is 8 thousandths or 0.008.

6. What is the value of 4 in 4.825?

Four thousandths

The digit 4 is in the ones column, so the value is 4 ones or 4.

Place value FAQ

Our number system is called Base Ten, because ten is the value used to create the place value groupings. That is why all of the place value positions (like the tens place or hundreds place) are multiples of 10. This is also why younger students practice skip counting by tens, which ultimately helps them recognize patterns in our number system.

Place value helps you understand the size of a number and gives meaning to the digits in each position. An understanding of place value can help you when comparing numbers and ordering numbers and is also essential when operating with numbers.

Per the Common Core, in fifth grade students work with the tenths place, the hundredths place and the thousandths place. Sixth graders should extend this to smaller positions. It is also important to be mindful of standard expectations, as they may vary from state to state.

The next lessons are

• Factors and multiples
• Fractions operations

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Place Value Word Problems

Read the Whole Word Problem: Firstly, read the entire word problem so you can understand it somewhat better. Then, ask yourself questions each time you’re confronted by a word problem. After that, check the work whenever you’re done.

A step-by-step guide to solving place value word problems

Here’s a step-by-step guide to solving place value word problems:

• Read the problem carefully and identify the given information: In a place value word problem, you are usually given a number or a set of numbers, along with some specific information about the digits or their positions. Read the problem carefully identify the given information, and make sure you understand what the problem is asking you to find.
• Identify the place value of the digits: The place value of a digit determines the value of the digit based on its position in the number. Identify the place value of the digits that are given or asked for in the problem. For example, if the problem involves finding the value of the hundreds place or the thousands place, make sure you know what these places are and how to calculate their values.
• Write the number in expanded form: Expanded form is a way of writing a number as the sum of its digits multiplied by its place values. Write the number in expanded form to help you visualize the value of each digit in the number.
• Perform the necessary operations: Once you have identified the given information and the place values of the digits, perform the necessary operations to solve the problem. This may involve adding, subtracting, multiplying, or dividing the digits to find the answer.
• Check your answer: After you have completed the problem, double-check your work to make sure your answer makes sense and is consistent with the problem. You can also verify your answer by using estimation or by working the problem backward.

The Absolute Best Book for 4th Grade Students

Mastering Grade 4 Math The Ultimate Step by Step Guide to Acing 4th Grade Math

By following these steps, you should be able to solve place value word problems with greater ease and accuracy.

The problem asks for a number that has 6 thousands, a number of hundreds that is 2 less than the number of thousands, a number of tens that is 1 more than the number of hundreds, and a number of ones that is 3 more than the number of thousands. What is this number?

Solution: You want to find the number 6 … … …

 2 fewer than a thousand is 4. 1 more tens than hundreds is 5. 3 more ones than thousands is 9.

So, it’s 6459.

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Mastering Grade 6 Math The Ultimate Step by Step Guide to Acing 6th Grade Math

Mastering grade 5 math the ultimate step by step guide to acing 5th grade math, mastering grade 3 math the ultimate step by step guide to acing 3rd grade math, mastering grade 5 math word problems the ultimate guide to tackling 5th grade math word problems, mastering grade 2 math word problems the ultimate guide to tackling 2nd grade math word problems, mastering grade 4 math word problems the ultimate guide to tackling 4th grade math word problems.

by: Effortless Math Team about 1 year ago (category: Articles )

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Place Value: How to Assess Students’ Understanding

If you’re familiar with Cooks Illustrated magazine, you know that they use their test kitchen to tinker with recipes and improve on them. In each issue, they report on all of the attempts they make and then finally present a recipe they recommend. In a way, I feel as if my search for a way to assess students’ understanding of place value has gone through a similar math teaching test kitchen.

By the end of first grade, students are expected to understand that the two digits of a two-digit number represent amounts of tens and ones. In second grade, they extend their understanding to three-digit numbers and the meaning of the digits in the hundreds, tens, and ones places.

First and second graders are generally familiar with numbers up to 100. Many can write the numbers from 1 to 100. Many can compare numbers—for example, 54 and 45—and tell which is greater. Many can identify which digit in two-digit numbers is in the tens place and which is in the ones place. These used to be the assessments I relied on for checking students’ understanding of place value, typically using worksheet assessments on which students filled in missing numbers, circled the greater numbers, and indicated whether digits were in the tens or ones place.

But once I began to spend time asking students questions, face to face, I found that while worksheet assessments might be helpful, interviews often produced surprising and sometimes disturbing evidence of shaky understanding.

For example, while students could fill in missing numbers correctly, when I asked them to count to 100, some were confused when changing from one decade to the next—for example, stumbling when they reached 29, not sure what came next. When I asked students to write a number like 38, some incorrectly would write 308 —writing  30 as they said “thirty” and then writing  8 as they said “eight.” While they could tell which digit was in the tens place and which digit was in the ones place, when comparing 54 and 45, for example, some could only offer the explanation that 54 is greater because “it comes after 45”—their explanations didn’t relate to the place values of the digits.

A More Reliable Way to Assess Convinced that worksheet assessments were not sufficient, I collaborated with a team of colleagues (special thanks to Mallika Scott and Lynne Zolli) to create a litmus test for finding out whether students have the necessary understanding of place value. We wanted the interview to be short (because the information is important to have for all students in the class), efficient (requiring a minimum of materials), and informative (giving clear information about students’ understanding). I’m not including here all the interview options we tried and eliminated, as the writers of Cooks Illustrated do for their recipes, but instead to cut to our current final version.

Last spring, when I spent a day in an elementary school in Brooklyn, NY, I used this as a baseline assessment to check second graders’ place value understanding with two-digit numbers. View how a few of the students responded.

Now What? My hope is that you’ll try this assessment with your students. My suggestion: Predict first for each of your students how you think he or she will respond. Then ask and see what you learn. I’d like to hear from you, and for all of you to hear from each other, so please post comments, results, surprises, and any questions you have.

After Interviewing, Then What? Incorporate into your class instruction investigations that help students build understanding of place value. In the new fourth edition of About Teaching Mathematics , I include a collection of suggestions for teaching place value on pages 344–358. Also, I rely regularly on the ideas presented in Teaching Arithmetic: Lessons for Introducing Place Value , which I wrote with Maryann Wickett. And for students who would benefit from additional intervention, Do The Math modules Addition/Subtraction A and B are extremely useful.

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Thanks, Marilyn, for sharing this Place Value interview assessment question. I am going to encourage our K-2 teachers so use it with their students. I am happy to report that some of them already use your AS Place Value book!

Are you familiar with the work of Dr. Michael Battista, specifically his books on Cognitive Based Assessments and Teaching? He has 6 books, 1 per content area, including Place Value, based upon his 10+ years of research on how students understand math. We have been using some of his paper and pencil assessments 1-on-1 with our K-5 students. They help us to understand each student’s level of understanding of the content and then we incorporate his teaching ideas to help address the needs of each student. We have found them particularly effective with Place Value.

Thanks for your feedback, and for the encouragement to dig into Michael Battista’s books.

I enjoy learning from these, but I teach kindergarten. Do you have ideas for me to help my students? I’m trying to do investigations but engage NY math has kinda taken over. They’re pretty good but I need some hands on stuff? Thanks. alice

For help with your Kindergarten students, I suggest Teaching Preschool and Kindergarten Math by Ann Carlyle and Brenda Mercado, two collegues of mine with vast and deep experience. The book comes with more than 20 video clips of interviews. Hope this helps.

Yes, a very revealing interview question. I might be inclined to then move onto another teen number and have the student count out the correct number of cubes to begin with to see if that makes a difference to the way they answer. This may prompt them to view the number as a whole set before they work with its partitions.

In the classroom I would be giving students such as Gabrielle and Dennis lots and lots of practice modelling two digit numbers with discrete materials (bundling sticks, beans in canisters, stacking cubes) and minimally structured materials (slavonic abacus, tens frames). It’s important that they are then able to talk about their models with peers and the teacher who should also model explicit explanations of the tens and the ones. This way students are developing the math concept alongside mathematical language to help cement the ideas and gain clarity.

THanks for the suggestions. Most often I have the students count out the cubes. Actually, I typically ask them to count out 10 cubes onto a sheet of paper. Next to the paper, on the desk, I place six cubes and ask them to count how many I have. Then I push mine onto their paper and ask, “How many cubes are there in all on the paper now?” That establishes the 16, but also lets me see if the student knows, without counting that 10 plus 6 more gives 16. I’ve found there’s no one best way to assess students and I continue to tinker.

I will be trying this with my first graders! Thank you!

When you mentioned interview questions both Nina and I were curious and hoping to learn more. I like how this question can uncover misconceptions. It’s like detective work. I recently saw a Richard Feynman quote “The first principle is that you must not fool yourself – and you are the easiest person to fool.” It’s easy to use a pencil and paper assessment without an interview and think that students understand. Time is gold in a classroom so I’m equally enthused that you’re finding interview q’s that are just as quick as they are informative. Is there any place for a number line in an interview like this?

This also makes me think about extending place value understanding from 0 – 100 to thousands, and beyond. I’ve seen some wild misconceptions with 4th graders and place value once the numbers get an order of magnitude or two larger. Think this assessment could scale up to larger numbers?

P.S. Keep the posts coming about other interview questions!

I’ve seen the same issues when ‘scaling up’ to larger numbers. Possibly hiding a weak or flawed conceptual understanding of PV in the 1-10-100-1000s Misconceptions that bigger numbers behave differently

Where have you noticed it? I never demanded the traditional subtraction algorithm but students knew it and used it. The interesting thing isn’t that they’d use the procedure correctly. It was that they could explain what was happening in the ones, and tens, maybe even hundreds but then say something non-sensical about the thousands. These noticings were from students reasoning at a wide range of levels.

I have my suspicions about the root causes but still much more to learn.

I teach multi-age students, 7 and 8 year Olds (2nd and 3rd grade) and will try this interview. I have been trained to teach CGI, but always struggling with once students are understanding a concept where to move them next. I can’t wait to read your research to help with my uncertainties. Thank you!

Thank you! I find this really interesting. I was listening to the language you used, and in Gabriela’s interview you said, “Show the 6 with 6 cubes… What the 6 means in 16.” Then with Dennis you said, “These 6 match the number 6. Can you show what matches #1?” I think that for many kids, place value is just about matching the numbers into 10s and 1s places and this interview can help us understand how they are thinking about the 10s and 1s. Many activities kids do to learn place value just have them identifying tens and ones, not actually building the numbers and seeing that they are composed of bundles of 10s and some 1s. It seems that having the child make the number themselves by counting out the right number of cubes by 1s would be important for the kids who are having a harder time holding on to both the 10s and 1s at the same time. For the purposes of giving us a quick sense of who is secure with this concept and who is shaky it seems effective. I might ask them to count out 26 next, and see if they can show that the 2 is both 20 and 2 10’s. Lots more packing experiences are needed in my opinion.

You’re correct that this is a suggestion for giving a quick sense of who is secure and who is shaky. Then I dig more deeply with students in several ways. As an example, see my response below to the comment from Michele Kire. For students who answer correctly to the assessment on the video clips, I also put 10 more cubes on the paper and ask students, “When I add 10 more cubes to the 16, how many will there be?” It’s interesting to see if they know or have to count. THanks for your post.

I like that idea. That way they’re not counting by ones. It’s such a good reminder that we have to watch young students do the math as much as possible in order to really know what they understand. The intuition that we get during an interview gives us a sense of a child’s understanding that a paper can’t show. If a child is secure with the concept, the exact words we say don’t matter to the same extent, (“show the 6, match the 6”) because I can see the confidence or lack thereof in his or her face.

About 6 years ago I saw this questions asked for the first time on a beginning of the year second grade interview assessment. I thought it was way to easy for kids at that age and for sure they would all get it right. I was so surprised that only 2 kids in the entire class were able to answer it correctly. Since then we have placed a variation of this question on both our first and second grade assessment interviews and it has made such a difference in how well we understand what kids get and don’t get about place value.

While reading the article about “Place Value: How to Assess Students’ Understanding” I liked the way how the writer uses metaphor of “Cooks Illustrated” magazine to describe students’ understanding of place value as teaching test kitchen. From the first grade to extensions of grades, learning about place value seems to be hard tasks for students. While reading this article, what I came to my mind is that the idea about “the multiplication of number 5 with even numbers disturb place value” which was covered in the lecture. As we see multiplication of number 5, it resulted in 5, 10, 15, 20, 25, 30, 35…… and so on. Therefore, when we get the equation like 5 times 60, some students make mistake of “extra zero.” To be specific, students think that there is 0 at the end, so they just put one zero without considering 5 times 6 is 30 which resulted in “two zeros”. By gathering information from example from the article and the example of article, I was able to gather information about how students can confused with math concepts and how can I adopt this in the future. Also, this also demonstrates the significance of core math concepts and teach them with conceptual understandings.

I’ve been a big fan of Marilyn Burns for YEARS and have followed her thinking closely. Many years ago I was teaching third grade in an upper middle class urban school and decided to assess the third graders familiarity with place value by using this interview method. I jotted down how comfortable they were with their answers. I was shocked when about 18 out of 24 children showed me one tile to represent the ‘1’ in 14. I shared this with the other third grade teachers. They were quick to declare that THEIR third graders would most certainly be able to such a simple assessment and they were SURE their third graders had a very firm grasp of place value. Only one of the 3 agreed to also assess her class. Imagine her surprise when she got similar results to mine. I assessed the third graders again in January and again in May. By May I had only 1 child who insisted it was one tile, folding her arms and glaring at me. I’m not sure we were actually addressing her math conceptual knowledge! I want to add that once a child (or anyone) has assimilated a concept they can’t be budged. So, if you change the interview and do it several different ways you should get similar results each time. Simply using a different question, or using a different number of tiles etc. should not give you hugely different answers. Thanks for the great blog!!

I’m currently working on a school-wide system to test fluency from Kindergarten through fifth grades. I’m really leaning towards the individual interview approach, but I’m having a hard time finding really good questions to ask at each grade level. I recently attending the 2017 KASA convention in Louisville, Kentucky and attending a session that consisted of a video conference with you. I remember these videos from that session, but I also remember you saying there were more videos, but I couldn’t remember where you said to find them. Any input would be most helpful, thanks!

You might be interested in the videos on Math Reasoning Inventory site. Click on the Resources tab, then scroll down and click on Video Library. Clips are sorted by questions and by students. Let me know if you’d like additional information.

I like the individual assessment, then you can tell if the child is progressing some thinking….

What would be some meaningful activities to use with the students who were not able to show the ten?

You may find some ideas in Teaching Arithmetic: Lessons for Introducing Place Value, Grade 2 and also the companion book, Lessons for Extending Place Value, Grade 3. Hope this helps.

I gave this place value interview assessment to a second grade boy and he was successful in showing the ten cubes as representing the one in the number 16. So I added a task and gave him a card with 16 + 10 written horizontally on it and asked him to read it and then work it out. He said: “18”. I asked how he got that answer and rather than explain his answer, he proceeded to count-on from 16, but he got “25” because he began his count with “16” on the first finger and continued counting using up his ten fingers. Then I asked him if he was sure and he recounted-on with his fingers and this time started with 17 he ended on “26” as the answer. He said, “How come I keep getting different answers?” I asked which answer he thought was correct and he said “18”. I asked him to show me how he got 18. His response: “16 and 0 is 16, then you add this one, 17 (pointing to the one in 16) and then that one (pointing to the one in 10) is 18.”

I know his teacher was teaching the algorithm for double-digit addition and this was evidence of a student trying to carrying out a taught procedure without any understanding.

But what do you make of his understanding with materials but not being able to add 10 more? Was it because it was a written equation that he just worked with the digits? What would be a good next question to dig further into a (2nd grade) student’s place value understanding?

Wow, this is so interesting. Several thoughts: After he counts the 16 cubes, instead of showing the 16 + 10 equation, what about asking, “If I give you ten more cubes, how many will you have?” Then he can verify with the cube. Then ask, “What if I give you ten more cubes?” Again, he can verify. After doing this, you might talk about how to write down “in math” what you did: 16 + 10 = 26; 26 + 10 = 36. Then try another problem, like 18 + 10, or maybe 16 + 30.

Also, I’m curious if you asked him, when he had the 16 cubes in front of him, “If you gave me 10, how many would you have left for yourself?”

All of these are clues. If you try them, send me his responses and we can think some more. And thanks for writing.

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Unit 1: Place value

About this unit.

We will learn about the ones, tens, and hundreds place values and compare 3-digit numbers.

Intro to place value

• Intro to place value (Opens a modal)
• Use place value blocks to show numbers within 1,000 (Opens a modal)
• Place value tables within 1,000 (Opens a modal)
• Identifying value in digits (Opens a modal)
• Creating the largest number (Opens a modal)
• Place value blocks within 1,000 Get 3 of 4 questions to level up!
• Place value tables within 1,000 Get 3 of 4 questions to level up!
• Identify the value of a digit (ones, tens, hundreds) Get 3 of 4 questions to level up!
• Create the largest number Get 3 of 4 questions to level up!

Numbers in standard, written, and expanded form

• Expanded form of numbers (Opens a modal)
• Number and word form of a number (Opens a modal)
• Word form and expanded form (Opens a modal)
• Write numbers in number and expanded form Get 3 of 4 questions to level up!
• Write numbers in number and word form Get 3 of 4 questions to level up!
• Write numbers in word and expanded form Get 3 of 4 questions to level up!
• Write numbers in different forms Get 3 of 4 questions to level up!

Regroup whole numbers

• Regrouping whole numbers: 675 (Opens a modal)
• Regroup whole numbers Get 3 of 4 questions to level up!
• Hundreds, tens, and ones Get 3 of 4 questions to level up!

Comparing 2 & 3-digit numbers

• Greater than and less than symbols (Opens a modal)
• Comparing whole numbers (Opens a modal)
• Compare 2-digit numbers Get 5 of 7 questions to level up!
• Compare 3-digit numbers Get 5 of 7 questions to level up!

Counting patterns within 1,000

• Skip-counting by 5s (Opens a modal)
• Counting by 10s (Opens a modal)
• Skip-counting by 100s (Opens a modal)
• Skip-count by 5s Get 5 of 7 questions to level up!
• Skip-count by 10s Get 5 of 7 questions to level up!
• Skip-counting by 100s Get 5 of 7 questions to level up!

Place-Value Concepts

This page contains resources to support teaching and learning of place-value concepts. Three videos draw on research-based frameworks to illuminate the rich and complex topic of place value and how children come to understand this topic. Additionally an interview protocol for diagnosing student understanding of place value is available along with video examples of students participating in that interview. Finally a list of additional resources is offered for those who wish to go further with study of this topic.

Educator Videos

The following three videos contain a discussion and synthesis of research-based frameworks that can be useful for making sense of student understanding of place-value concepts and an interview protocol in PDF format used to assess students understanding of place value during these interviews.

The Multifaceted Nature of Place Value: It’s About More Than Digit Values

11:56 / View on YouTube / Download Transcript

The Child’s Perspective on Place Value: Five Ways Children Conceptualize Two-Digit Numbers

12:08 / View on YouTube / Download Transcript

Provoking Place-Value Reasoning with Groups of Ten Word Problems: Excerpts from Ms. Brannon’s First Grade Class

14:41 / View on YouTube / Download Transcript

Place-Value Assessment Resources

Click the thumbnails to access resources to support assessment of students’ understanding of place-value in a base-ten number system. The assessment designed to be used in a one-on-one interview setting. Blackline masters are also available in the downloadable file. The downloadable diagram provides a conceptual model for the various components of place-value understanding that occur over a period of several years of school mathematics.

Student Videos

The following three videos show a kindergarten student, a first-grade student, and a second-grade student engaged in the place-value interview.

Kindergarten – Tim

19:51 / View on YouTube / Download Transcript

First Grade – Weston

30:00 / View on YouTube / Download Transcript

Second Grade – Valerie

23:47 / View on YouTube / Download Transcript

Resources for Further Study of Place Value

Click the following titles to access a short list of teacher resource books and journal articles that were reviewed in preparation of these resources.

Teacher Resource Books

• This book details research findings on the development of children’s mathematical thinking in relation to the four operations (addition subtraction multiplication and division) and base-ten number concepts.
• Chapter one of this book includes ideas for teaching and assessing place-value concepts. The book also contains a collection of activities focused on providing children with a variety of experiences generating strategies for organizing large quantities into tens and ones.
• This book includes a collection of ideas for teaching and assessing place-value concepts. Lessons are organized into three main types: Counting and grouping activities number chart activities and activities focused on exchanging ones and tens. The assessments chapter contains suggestions for tasks to use in an individual interview.
• Chapter eleven of this book includes discussion of children’s development of whole-number place-value concepts and ideas for instruction and assessment related to these concepts.
• This article illustrates how contextualized problems involving groups of ten can be used to advance early elementary students’ understanding of place-value concepts.
• This article introduces a set of strategic counting tasks’ to use for the purpose of assessing children’s place-value understanding. The authors discuss the advantages of the strategic counting tasks over other tasks commonly used to assess place-value understanding and detail findings of three research studies that used this set of tasks.
• Drawing on data from four research projects implementing a problem-solving approach to teaching and learning multidigit number concepts and operations this article presents a framework of conceptual structures that articulate different ways children think about multidigit numbers. The article also discusses categories of methods children devise to solve multidigit addition and subtraction problems. The research in this article forms the basis of the ideas presented in  The Child’s Perspective on Place Value: Five Ways Children Conceptualize Two-Digit Numbers (see above).
• This article draws on the work of multiple research projects to identify curricular elements essential for the development of place-value understanding. A framework is suggested for nurturing and assessing place-value understanding in the early elementary grades.
• This article describes findings of two studies utilizing digit-correspondence tasks to explore students’ understanding of the meaning of the digits in two-digit numbers. Implications for the classroom are also discussed.
• This article describes findings from a classroom study that explores the effects of classroom lessons involving digit-correspondence tasks on students’ understanding of the meaning of the digits in two- and three-digit numbers.

Place Value – Definition with Examples

What is place value, place value chart, what is the difference between place value and face value, solved examples on place value, practice problems on place value, frequently asked questions on place value.

In math, every digit in a number has a place value. Place value can be defined as the value represented by a digit in a number on the basis of its position in the number .

For example, the place value of 7 in 3,743 is 7 hundred or 700. However, the place value of 7 in 7,432 is 7 thousand or 7,000. Here, we can see that even though the digits are the same in both numbers, their place value changes with the change in its position. 

Place Value Chart is a very useful table format that helps us in finding the place value of each digit based on its position in a number. 

The place value of a digit increases by ten times as we move left on the place value chart and decreases by ten times as we move right.  

Here’s an example of how drawing the place value chart can help in finding the place value of a number. 

In the number 13,548

1 is in the ten thousands place and has a place value of 10,000.

3 is in the thousands place and has a place value of 3,000.

5 is in the hundreds and has a place value of 500.

4 is in the tens place and has a place value of 40.

8 is in the ones place and has a place value of 8.

Understanding the place value of digits in numbers helps comparing numbers. It also helps in writing numbers in their expanded form. For instance, the expanded form of the number above, 13,548 is 10,000 + 3,000 + 500 + 40 + 8. 

Related Worksheets

Place Value Using Base Ten Blocks

The place value of digits in numbers can also be represented using base-ten blocks and can help us write numbers in their expanded form.

Before, using the base ten blocks to find the place value of each digit in a number, let us first understand what these blocks represent.

Here’s how the number 13,548 can be represented using base-ten blocks.

Decimal Place Value

Decimal numbers are fractions or mixed numbers with denominators of powers of ten . In a decimal number , the digits to the left of the decimal point represent a whole number . The digits to the right of the decimal represent the parts. As we move towards right after the decimal point, the place value of the digits becomes 10 times smaller.

The first digit on the right of the decimal point means tenths i.e. 110. The next place becomes ten times smaller and is called the hunderdths i.e. 1100 and so on. 

In 27.356, 27 is the whole number part, 2 is in tens place and its place value is 20,7 is in ones place, and its place value is 7. 

There are three digits to the right of the decimal point ,               

3 is in the tenths place, and its place value is 0.3 or 3 10

5 is in the hundredths place, and its place value is 0.05 or 5100

6 is in the thousandths place, and its place value is 0.006 or 61000

Place value and face value are not the same. The face value of a digit is the value of the digit, whereas the place value of a digit is its place in the number. In simple words, the face value tells the actual value of the digit, whereas the place value tells the value of the digit based on its position. 

Hence, the face value of the digit never changes irrespective of it’s position in the number. Whereas, the place value of the digit changes with the change in the position. 

For instance, the face value of 2 in both the numbers 283 and 823 is 2. Whereas, the place value of 2 is 200 in 283 and 20 in 823. 

•   What is the place value of 4 in the number 84,527?

The place value of 4 in 84,527 is 4000 (four thousand).

•   Write 412,397 in words using the place value system.

Four hundred twelve thousand three hundred and ninety-seven.

• Write the numbers in figures and in expanded form :
• Ten thousand two hundred and thirty-six
• Seven thousand four hundred and eighty-five
• Ten thousand two hundred and thirty-six = 10,236

= 10,000 + 200 + 30 + 6

• Seven thousand four hundred and eighty-five = 7,485

= 7,000 + 400 + 80 + 5

Place Value

Attend this Quiz & Test your knowledge.

Which digit is at the ten thousands place in the number 783,425?

Select the correct answer in standard form. $40,000 + 4,000 + 200 + 10 + 1$, what will be the place value of 8 in the number 13.86.

Why is understanding place value important?

Place value has its application in many mathematical concepts. It builds the foundation for regrouping , multiplication , etc.

What manipulatives are used to teach place value?

Manipulatives such as base-10 blocks, snap cubes, unifix cubes, beans, etc., are used to develop place value understanding.

Does the place value of a digit increase as it moves from left to right?

No. The place value of a digit decreases by 10 times as it moves from left to right.

What is the difference between the face value and the place value of a digit?

The face value of a digit is the magnitude that it possesses naturally. It is independent of the digit’s position in the number. The place value of a digit depends on its position in the number. For example, the 5 in the number 253 has a face value of 5 and a place value is 50.

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