Converting Fractions to Decimals
Learn how to convert any fraction into a decimal using division.
Definition
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Worked Examples
Convert to a decimal.
Set up the division
→ Numerator divided by denominator
Perform the division
→
Verify your answer
✓ → Correct!
Answer:
Common Mistakes
Dividing the denominator by the numerator instead
Why it's wrong: Students sometimes reverse the division: doing instead of for .
Correct: Always divide the TOP number (numerator) by the BOTTOM number (denominator). Think: the fraction bar means 'divided by'.
Forgetting to add zeros when dividing
Why it's wrong: When doesn't work as a whole number, students get stuck.
Correct: Add a decimal point and zeros: . You can always add zeros after a decimal point.
Stopping the division too early
Why it's wrong: Students might write instead of completing the division to get .
Correct: Keep dividing until there's no remainder OR you see a repeating pattern.
Confusing decimal places with fraction parts
Why it's wrong: Writing as by just placing the numbers.
Correct: You must DIVIDE! , not .
Interactive Visual
Click on the circle to change the fraction
Place Value Chart
| Ones 1 | Tenths 0.1 | Hundredths 0.01 |
|---|---|---|
| 0 | 7 | 5 |
Expanded Form:
7 × 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
15 problemsWhat is as a decimal?
Why It Matters
- Shopping: A sale offering off is the same as 25% or 0.25 off the price
- Cooking: A recipe calls for cup, but your measuring cup shows decimals (0.75)
- Sports: A basketball player makes of free throws, which is 0.7 or 70%
- Grades: Scoring on a test equals 0.85 or 85%
Real World Applications
Shopping Discounts
Stores often express discounts as fractions, but calculators use decimals.
Example:
A jacket costs 80 dollars with off. Since , the discount is dollars.
A video game is 60 dollars with off.
What is the discount amount?
Step 1: Write the mathematical expression
First convert to a decimal, then multiply:
Cooking Measurements
Recipes use fractions, but digital scales show decimals.
Example:
A recipe needs cup of flour. Your digital measuring cup shows this as 0.75 cups.
You need cup of sugar. Your measuring cup shows decimals.
What decimal should you measure to?
Step 1: Write the mathematical expression
Convert to a decimal:
Test Scores
Teachers often convert fraction scores to decimals for calculating grades.
Example:
Getting correct means or 90%.
You scored on a quiz.
What is your score as a decimal?
Step 1: Write the mathematical expression
Divide the numerator by the denominator:
Key Takeaways
- 1To convert a fraction to a decimal, divide the numerator by the denominator
- 2The fraction bar means 'divided by':
- 3Add zeros after the decimal point if needed to complete the division
- 4Common conversions to memorize: , , ,
Frequently Asked Questions
Glossary
- Numerator
- The top number in a fraction, showing how many parts you have
- Denominator
- The bottom number in a fraction, showing how many equal parts make a whole
- Terminating decimal
- A decimal that ends, like or
- Equivalent
- Having the same value, just written differently ( and are equivalent)
Formula Card
Fraction to Decimal
Divide the numerator (top) by the denominator (bottom). Example: $\frac{3}{4} = 3 \div 4 = 0.75$