Converting Between Fractions and Decimals
What Is This?
Fractions and decimals are two different ways of writing the same value. Converting between them means rewriting one form as the other without changing the amount. 1/2 and 0.5 are the same number — they just look different. Knowing how to move fluently between both forms is one of the most useful skills in all of mathematics.
Why Does It Matter?
Calculators work in decimals. Recipes use fractions. Measurements mix both. Being able to convert freely lets you compare values, solve mixed problems, and check answers regardless of which form they appear in. It also ties together everything you have learned about fractions and decimals in this unit.
Part 1 — Fraction to Decimal
There are three methods. Choose the one that suits the fraction.
Method A — Denominator is Already 10 or 100
Write the numerator directly in the matching decimal place.
| Fraction | Denominator | Decimal |
|---|---|---|
| 3/10 | 10 → tenths | 0.3 |
| 7/10 | 10 → tenths | 0.7 |
| 9/100 | 100 → hundredths | 0.09 |
| 43/100 | 100 → hundredths | 0.43 |
Method B — Convert the Denominator to 10 or 100
If the denominator is a factor of 10 or 100, multiply both numerator and denominator to reach 10 or 100.
Example: 3/5
- 5 × 2 = 10, so multiply both by 2
- 3/5 = 6/10 = 0.6
Example: 3/4
- 4 × 25 = 100, so multiply both by 25
- 3/4 = 75/100 = 0.75
Example: 7/20
- 20 × 5 = 100, so multiply both by 5
- 7/20 = 35/100 = 0.35
Denominators that work with Method B: 2, 4, 5, 10, 20, 25, 50, 100.
Method C — Divide the Numerator by the Denominator
This method works for any fraction. Divide the top number by the bottom number.
Example: 3/8
- 3 ÷ 8 = 0.375
Example: 5/6
- 5 ÷ 6 = 0.8333… (a repeating decimal)
Example: 7/8
- 7 ÷ 8 = 0.875
Long division set-up:
0 . 8 7 5
8 ) 7 . 0 0 0
Part 2 — Decimal to Fraction
Step 1 — Write the decimal as a fraction using place value
| Decimal | Read as | Fraction |
|---|---|---|
| 0.3 | three tenths | 3/10 |
| 0.07 | seven hundredths | 7/100 |
| 0.45 | forty-five hundredths | 45/100 |
| 0.6 | six tenths | 6/10 |
Step 2 — Simplify to lowest terms
Divide numerator and denominator by their GCF.
Example: 0.6 = 6/10 → GCF = 2 → 3/5
Example: 0.75 = 75/100 → GCF = 25 → 3/4
Example: 0.08 = 8/100 → GCF = 4 → 2/25
Example: 0.35 = 35/100 → GCF = 5 → 7/20
Quick-Reference Conversion Chart
Memorising these common conversions saves time and helps you estimate quickly.
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/2 | 0.5 | 1/8 | 0.125 |
| 1/4 | 0.25 | 3/8 | 0.375 |
| 3/4 | 0.75 | 5/8 | 0.625 |
| 1/5 | 0.2 | 7/8 | 0.875 |
| 2/5 | 0.4 | 1/10 | 0.1 |
| 3/5 | 0.6 | 1/100 | 0.01 |
| 4/5 | 0.8 | 1/3 | 0.333… |
| 1/20 | 0.05 | 2/3 | 0.666… |
Worked Examples
Worked Example 1: Convert 9/20 to a decimal
- 20 × 5 = 100 → multiply both by 5
- 9/20 = 45/100 = 0.45
Worked Example 2: Convert 5/8 to a decimal
- 8 does not divide into 10 or 100 → use division
- 5 ÷ 8 = 0.625
Worked Example 3: Convert 0.35 to a fraction in simplest form
- 0.35 = 35/100
- GCF(35, 100) = 5
- 35 ÷ 5 = 7; 100 ÷ 5 = 20
- 7/20
Worked Example 4: Convert 0.125 to a fraction in simplest form
- 0.125 = 125/1000
- GCF(125, 1000) = 125
- 125 ÷ 125 = 1; 1000 ÷ 125 = 8
- 1/8
Worked Example 5: Which is larger — 5/8 or 0.6?
- Convert 5/8 to decimal: 5 ÷ 8 = 0.625
- Compare: 0.625 vs 0.6
- 0.625 > 0.6, so 5/8 > 0.6 ✓
Choosing the Right Method
| Fraction | Best method |
|---|---|
| 7/10, 43/100 | Method A — denominator already 10 or 100 |
| 3/4, 2/5, 7/20 | Method B — convert denominator to 10 or 100 |
| 3/8, 5/6, 7/11 | Method C — divide numerator by denominator |
Common Mistakes
Mistake 1: Writing 3/5 as 0.3 You cannot just move the numerator into the tenths place. 3/5 = 6/10 = 0.6, not 0.3. Always convert the denominator first.
Mistake 2: Forgetting to simplify 0.75 = 75/100 is correct but not fully simplified. Always divide by the GCF: 75/100 ÷ 25/25 = 3/4.
Mistake 3: Confusing tenths and hundredths 0.7 = 7/10, but 0.07 = 7/100. The number of digits after the decimal point tells you the denominator: 1 digit → /10; 2 digits → /100; 3 digits → /1000.
Mistake 4: Stopping division too early 3/8: 3 ÷ 8. If you stop at 0.37, the answer is wrong. Keep adding zeros and dividing until the remainder is zero (or the pattern repeats).
Key Takeaways
- Fraction → Decimal: use Method A (denominator 10/100), Method B (scale denominator to 10/100), or Method C (divide numerator by denominator)
- Decimal → Fraction: write using place value (tenths, hundredths), then simplify by dividing by the GCF
- The number of decimal places tells you the denominator: 1 place = /10, 2 places = /100, 3 places = /1000
- Memorise the common conversions: halves, quarters, fifths, eighths
- Converting to the same form lets you compare fractions and decimals directly
Practice and Resources
Ready to practise? Try our Grade 3-5 Converting Fractions and Decimals Worksheet with problems covering all three methods and simplification. Test yourself with the Grade 3-5 Math Practice Test.