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: Position determines value - the same digit means different amounts in different places.

Common stuck point: Confusing the digit with its place value: in 352, the digit 3 has value 300, not 3.

Sense of Study hint: Write out the expanded form: break 352 into 300 + 50 + 2 to see what each digit is really worth.

Worked Examples

Example 1

easy
Write the number 4{,}072 in expanded form.

Solution

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

Answer

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

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?
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Background Knowledge

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

countingnumber sense