Comparing Decimals

Learn how to compare decimal numbers using place value and the number line.

Elementary15 minLesson
Printable worksheet

Definition

Comparing decimals means deciding which decimal is greater, which is lesser, or if they are equal.
We use comparison symbols:
  • >> means "greater than"
  • << means "less than"
  • == means "equal to"
To compare decimals:
  1. 1.Line up the decimal points
  2. 2.Compare digit by digit from left to right
  3. 3.Add zeros if needed to make the same number of decimal places
0.7>0.5(7 tenths is more than 5 tenths)0.7 > 0.5 \quad \text{(7 tenths is more than 5 tenths)}

Try it now

Which symbol makes this statement true? 0.7 □ 0.40.7 \, \square \, 0.4

Worked Examples

Which is greater: 0.60.6 or 0.40.4?
1

Look at the ones place

Both have 00 in the ones place → Ones are equal
2

Compare the tenths place

66 tenths vs 44 tenths → 6>46 > 4
3

Write the comparison

Since 6>46 > 4, we have 0.6>0.40.6 > 0.4

Common Mistakes

Thinking 0.17>0.90.17 > 0.9 because 17>917 > 9

Why it's wrong: Students sometimes ignore the decimal point and compare as if they were whole numbers.

Correct: Line up decimal points: 0.170.17 vs 0.900.90. Since 1<91 < 9 in the tenths place, 0.17<0.90.17 < 0.9

Thinking more digits means a larger number

Why it's wrong: Having more decimal places doesn't mean a larger value. Place value matters!

Correct: 0.50.5 (one decimal place) is greater than 0.4320.432 (three decimal places) because 5>45 > 4 in tenths

Forgetting to add trailing zeros when comparing

Why it's wrong: Different decimal places make comparison harder.

Correct: Write 0.30.3 as 0.300.30 to compare with 0.280.28. Now it's clear: 30>2830 > 28 hundredths

Interactive Visual

to

Click on numbers to select them. Adjust the range to explore different values.

Place Value Chart

Enter a number:

0.47
Ones
1
Tenths
0.1
Hundredths
0.01
047

Expanded Form:

4 × 0.1 + 7 × 0.01

Click on any place value to highlight it and see its value.

Interactive Sandbox

Expression Calculator

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Practice Problems

16 problems
Problem 1 of 16
Easy
Which symbol makes this statement true? 0.7 □ 0.40.7 \, \square \, 0.4

Why It Matters

Comparing decimals is essential in everyday life:
  • Shopping: Is 0.99 dollars less than 1.05 dollars? (Yes!)
  • Sports: A race time of 10.52 seconds beats 10.61 seconds
  • Cooking: Knowing that 0.25 cups is less than 0.5 cups
  • Science: Comparing measurements like 2.35 cm vs 2.4 cm
Understanding decimal comparison helps you make smart decisions with money, time, and measurements!

Real World Applications

Shopping and Prices

Comparing prices to find the best deal requires decimal comparison.

Example:

A store sells pencils for 0.75 dollars and pens for 0.80 dollars. Which costs less?

1Try It Yourself

You're comparing prices: Product A costs 2.49 dollars and Product B costs 2.5 dollars.

Which product costs less?

Step 1: Choose the right answer

Which comparison of 2.492.49 and 2.502.50 is true?

Sports Times and Scores

In racing and gymnastics, small decimal differences determine winners.

Example:

Runner A finishes in 12.45 seconds, Runner B in 12.39 seconds. Runner B wins because 12.39<12.4512.39 < 12.45.

2Try It Yourself

Two gymnasts score 9.85 and 9.9. Who scored higher?

Which score is higher?

Step 1: Choose the right answer

Which comparison of 9.859.85 and 9.909.90 is true?

Key Takeaways

  • 1To compare decimals, line up the decimal points and compare digit by digit from left to right
  • 2Add trailing zeros to make decimals have the same number of places: 0.5=0.50=0.5000.5 = 0.50 = 0.500
  • 3The first place where digits differ determines which number is greater
  • 4More decimal places does NOT mean a larger number: 0.9>0.8750.9 > 0.875

Frequently Asked Questions

Yes! Adding zeros to the right of the last decimal digit doesn't change the value. 0.5=0.50=0.5000.5 = 0.50 = 0.500
Yes! Adding zeros to the right of the last decimal digit doesn't change the value. 0.5=0.50=0.5000.5 = 0.50 = 0.500
Write them with the same decimal places: 0.090.09 vs 0.100.10. Since 9<109 < 10 hundredths, 0.09<0.10.09 < 0.1
Write 0.30.3 as 0.300.30. Now compare: 3030 hundredths vs 2929 hundredths. Since 30>2930 > 29, we have 0.3>0.290.3 > 0.29

Glossary

Decimal
A number written with a decimal point; the digits after the point show parts smaller than one whole (e.g., 0.750.75, 3.143.14)
Place value
The value of a digit based on its position (ones, tenths, hundredths, etc.)
Greater than (>)
A symbol showing the first number is larger: 5>35 > 3
Less than (<)
A symbol showing the first number is smaller: 2<72 < 7
Today's challengeOne problem, three tries

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