Decimal Place Value Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Decimal 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 assigned to each digit's position to the right of the decimal point: the first position is tenths (\frac{1}{10}), the second is hundredths (\frac{1}{100}), the third is thousandths (\frac{1}{1000}), and so on.

Just as moving left of the decimal point makes each place 10 times bigger (ones, tens, hundreds), moving right makes each place 10 times smaller (tenths, hundredths, thousandths). It's like zooming in—each step splits things into 10 equal pieces.

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: Each position to the right of the decimal point is one-tenth the value of the position to its left.

Common stuck point: Thinking that more decimal digits always means a larger number (0.45 vs 0.9: students may think 0.45 > 0.9 because 45 > 9).

Sense of Study hint: When you see a decimal, write each digit under its place-value label (ones, tenths, hundredths). First identify which column each digit belongs to. Then multiply each digit by its place value. Finally, add the results to find the total value.

Worked Examples

Example 1

easy
In the number 4.73, identify the value of each digit.

Solution

  1. 1
    4 is in the ones place: value = 4.
  2. 2
    7 is in the tenths place: value = \(\frac{7}{10} = 0.7\).
  3. 3
    3 is in the hundredths place: value = \(\frac{3}{100} = 0.03\).
  4. 4
    Total: \(4 + 0.7 + 0.03 = 4.73\).

Answer

4 ones, 7 tenths, 3 hundredths
Place value tells us what a digit is worth. Moving right of the decimal point: tenths (÷10), hundredths (÷100), thousandths (÷1000), etc.

Example 2

medium
Write 3 hundredths, 5 tenths, and 2 ones as a single decimal number.

Example 3

medium
In the number 45.0372, what is the place value of the digit 3?

Practice Problems

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

Example 1

easy
What is the value of the digit 6 in the number 1.63?

Example 2

medium
Order these decimals from least to greatest: 0.8, 0.08, 0.80, 0.008.
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Background Knowledge

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

place value