Place Value Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Place Value.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The value a digit represents based on its position in a number; the same digit means different amounts in different places.

In 352, the 3 is worth 300 because it's in the hundreds place.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A digit's value is the digit times the power of ten its column stands for.

Common stuck point: The procedure for place value is the easy part; the trap is adding the digits instead of weighting them by place. Asking "Does the worth of this digit depend on which column it sits in?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Does the worth of this digit depend on which column it sits in?

Worked Examples

Example 1

easy

Write the number

4{,}072

in expanded form.

Answer

4 \times 1000 + 7 \times 10 + 2 \times 1

First step

Identify each digit and its place: 4 is in the thousands place, 0 is in the hundreds place, 7 is in the tens place, 2 is in the ones place.

Full solution

2
Expanded form: $4 \times 1000 + 0 \times 100 + 7 \times 10 + 2 \times 1$ .
3
Simplify: $4000 + 0 + 70 + 2 = 4{,}072$ .

Expanded form reveals the place value of every digit. The zero in the hundreds place is a placeholder — it contributes

0 \times 100 = 0

but is essential for correct positional meaning of the other digits.

Example 2

medium

In the number

3{,}456{,}789

, what is the value of the digit

4

Example 3

medium

What is the value of the digit 7 in the number

473{,}218

Example 4

easy

You see 2 stars. How many stars?

Example 5

medium

Show 3 with your fingers. How many fingers?

Example 6

easy

Mia has 1 stick of ten and 2 single sticks. How many sticks total?

Example 7

easy

Show

16

as one ten and some ones. How many ones?

Example 8

medium

Which is bigger:

11

13

Example 9

easy

Decompose

58

into tens and ones.

Example 10

easy

Tess has 3 ten-sticks and 5 single cubes. How many cubes in all?

Example 11

hard

Sam has 2 tens and 15 ones. What number does Sam have?

Example 12

easy

A place-value chart shows 2 hundreds, 4 tens, and 6 ones. What is the number?

Example 13

easy

Write the number that has 6 hundreds, 0 tens, and 8 ones.

Example 14

hard

Using the digits

2

7

, and

5

exactly once each, what is the largest three-digit number you can make? What is the smallest?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

What number is 100 more than

2{,}897

Example 2

medium

A number has 5 in the thousands place, 0 in the hundreds place, 3 in the tens place, and 8 in the ones place. What is the number?

Example 3

easy

In the number

476

, what is the value of the digit

7

Example 4

easy

What digit is in the hundreds place of

8{,}352

Example 5

easy

Write the number that has

4

hundreds,

0

tens, and

9

ones.

Example 6

easy

5{,}284

, what is the value of the

5

Example 7

easy

How many tens are in

63

Example 8

easy

Write

307

in expanded form.

Example 9

easy

Which is greater:

89

98

Example 10

easy

What is

10

more than

267

Example 11

medium

What is

100

less than

543

Example 12

medium

4{,}040

, are the two

4

s worth the same? Explain.

Example 13

medium

Write the number that has

2

thousands,

7

hundreds,

0

tens, and

5

ones.

Example 14

medium

Which is greater:

4{,}089

4{,}098

Example 15

medium

What is the value of the digit

6

61{,}408

Example 16

medium

Write

9{,}000 + 200 + 3

as a single number.

Example 17

medium

How many ones are in

7{,}000

Example 18

medium

Round

478

to the nearest hundred.

Example 19

medium

What number is shown by

3

tens,

14

ones?

Example 20

challenge

I'm a three-digit number. My ones digit is twice my tens digit. My hundreds digit is the sum of the other two. The sum of all three digits is

6

. What number am I?

Example 21

challenge

Using the digits

3, 5, 8

exactly once each, what is the largest three-digit number you can make? What is the smallest?

Example 22

challenge

What is the smallest whole number greater than

999

that uses four different digits?

Example 23

easy

Count the cubes:

\square\square\square

. How many?

Example 24

easy

Show 4 with your fingers. How many fingers are up?

Example 25

easy

Which numeral is this:

5

Example 26

easy

Count the dots:

\bullet\,\bullet

. How many?

Example 27

medium

You have 5 grapes. How many grapes?

Example 28

hard

You see 5 ducks. How many ducks?

Example 29

easy

Ten and 3 ones. What number is that?

Example 30

easy

Ten and 5 ones. What number is that?

Example 31

easy

What does the

1

14

stand for?

Example 32

medium

Ten and 9 ones. What number is that?

Example 33

medium

Leo built 1 tower of ten and 8 extra cubes. How many cubes total?

Example 34

easy

What number is 4 tens and 7 ones?

Example 35

easy

How many tens are in

63

Example 36

easy

What number is 9 tens and 0 ones?

Example 37

medium

What is

10

more than

42

Example 38

medium

Write

86

as tens plus ones.

Example 39

easy

In the number

347

, what digit is in the hundreds place?

Example 40

easy

What is the value of the digit

5

581

Example 41

easy

Write

703

in expanded form.

Example 42

medium

What is

100

more than

456

Example 43

medium

What number is

200 + 50 + 4

in standard form?

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Related Concepts

Counting Number Sense Addition Decimals

Background Knowledge

These ideas may be useful before you work through the harder examples.

countingnumber sense