Comparing Decimals
Learn how to compare decimal numbers using place value and the number line.
Definition
- means "greater than"
- means "less than"
- means "equal to"
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Worked Examples
Which is greater: or ?
Look at the ones place
Both have in the ones place → Ones are equal
Compare the tenths place
tenths vs tenths →
Write the comparison
Since , we have →
Answer: is greater than
Common Mistakes
Thinking because
Why it's wrong: Students sometimes ignore the decimal point and compare as if they were whole numbers.
Correct: Line up decimal points: vs . Since in the tenths place,
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: (one decimal place) is greater than (three decimal places) because in tenths
Forgetting to add trailing zeros when comparing
Why it's wrong: Different decimal places make comparison harder.
Correct: Write as to compare with . Now it's clear: hundredths
Interactive Visual
Click on numbers to select them. Adjust the range to explore different values.
Place Value Chart
| Ones 1 | Tenths 0.1 | Hundredths 0.01 |
|---|---|---|
| 0 | 4 | 5 |
Expanded Form:
4 × 0.1 + 5 × 0.01
Click on any place value to highlight it and see its value.
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
16 problemsWhich symbol makes this statement true?
Why It Matters
- 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
Real World Applications
Shopping and Prices
Comparing prices to find the best deal requires decimal comparison.
Example:
A store sells pencils for 0.75 euros and pens for 0.80 euros. Which costs less?
You're comparing prices: Product A costs 2.49 euros and Product B costs 2.5 euros.
Which product costs less?
Step 1: Write the mathematical expression
Compare and
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 .
Two gymnasts score 9.85 and 9.9. Who scored higher?
Which score is higher?
Step 1: Write the mathematical expression
Compare and
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:
- 3The first place where digits differ determines which number is greater
- 4More decimal places does NOT mean a larger number:
Frequently Asked Questions
Glossary
- Decimal
- A number with a decimal point showing values less than one (e.g., , )
- 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:
- Less than (<)
- A symbol showing the first number is smaller: