Converting between fractions and decimals is a foundational skill that comes up in cooking, carpentry, finance, and everyday maths. This guide covers every method with worked examples.
Method 1: Long Division
The universal method — works for any fraction.
Divide the numerator by the denominator.
Example: Convert 3/8 to a decimal.
3 ÷ 8 = ?
Since 3 < 8, write 3.000 and divide:
- 8 goes into 30 → 3 times (3 × 8 = 24), remainder 6
- 8 goes into 60 → 7 times (7 × 8 = 56), remainder 4
- 8 goes into 40 → 5 times (5 × 8 = 40), remainder 0
3/8 = 0.375
Method 2: Convert to a Power-of-10 Denominator
Works when the denominator has only factors of 2 and 5 (i.e., can be made into 10, 100, 1000, etc.).
Example: Convert 7/20 to a decimal.
20 × 5 = 100, so multiply both numerator and denominator by 5:
(7) / (20) = (7 × 5) / (20 × 5) = (35) / (100) = 0.35
Example: Convert 3/4 to a decimal.
4 × 25 = 100:
(3) / (4) = (75) / (100) = 0.75
Example: Convert 7/8 to a decimal.
8 × 125 = 1000:
(7) / (8) = (875) / (1000) = 0.875
Terminating vs Recurring Decimals
Terminating decimals end after a finite number of digits: 1/4 = 0.25, 3/8 = 0.375.
A fraction produces a terminating decimal only when its denominator (in lowest terms) has no prime factors other than 2 and 5.
Recurring decimals repeat forever. They're written with a dot or bar over the repeating part:
(1) / (3) = 0.3̄ = 0.3333...
(1) / (7) = 0.142857̄ = 0.142857142857...
Any fraction with a prime denominator other than 2 or 5 will produce a recurring decimal.
Common Fraction to Decimal Reference Chart
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/2 | 0.5 | 1/9 | 0.111... |
| 1/3 | 0.333... | 2/9 | 0.222... |
| 2/3 | 0.666... | 1/10 | 0.1 |
| 1/4 | 0.25 | 1/11 | 0.0909... |
| 3/4 | 0.75 | 1/12 | 0.0833... |
| 1/5 | 0.2 | 5/12 | 0.4166... |
| 2/5 | 0.4 | 7/12 | 0.5833... |
| 3/5 | 0.6 | 1/16 | 0.0625 |
| 4/5 | 0.8 | 3/16 | 0.1875 |
| 1/6 | 0.1666... | 5/16 | 0.3125 |
| 5/6 | 0.8333... | 7/16 | 0.4375 |
| 1/7 | 0.142857... | 1/20 | 0.05 |
| 1/8 | 0.125 | 1/25 | 0.04 |
| 3/8 | 0.375 | 1/32 | 0.03125 |
| 5/8 | 0.625 | 1/50 | 0.02 |
| 7/8 | 0.875 | 1/100 | 0.01 |
Converting Decimals Back to Fractions
Terminating decimals
Count the decimal places, use that as the denominator power of 10, then simplify.
Example: 0.375
- Three decimal places → denominator 1000
- 0.375 = 375/1000
- GCD(375, 1000) = 125
- 375/1000 = 3/8 ✓
Example: 0.625
- 625/1000, GCD = 125
- 5/8 ✓
Recurring decimals
Example: Convert 0.333... to a fraction.
Let x = 0.333...
Multiply both sides by 10: 10x = 3.333...
Subtract: 10x − x = 3.333... − 0.333...
9x = 3
x = 3/9 = 1/3 ✓
Example: Convert 0.142857142857... to a fraction.
This has a 6-digit repeating block, so multiply by 10^6 = 1,000,000:
Let x = 0.142857142857...
1,000,000x = 142857.142857...
1,000,000x − x = 142857
999,999x = 142857
x = 142857/999,999 = 1/7 ✓
Fractions in Measurement (Imperial)
Imperial measurements use fractions constantly. Key conversions for woodworking, cooking, and construction:
| Inches (fraction) | Decimal inches | mm |
|---|---|---|
| 1/64" | 0.015625" | 0.397 mm |
| 1/32" | 0.03125" | 0.794 mm |
| 1/16" | 0.0625" | 1.588 mm |
| 1/8" | 0.125" | 3.175 mm |
| 3/16" | 0.1875" | 4.763 mm |
| 1/4" | 0.25" | 6.350 mm |
| 5/16" | 0.3125" | 7.938 mm |
| 3/8" | 0.375" | 9.525 mm |
| 7/16" | 0.4375" | 11.113 mm |
| 1/2" | 0.5" | 12.700 mm |
| 9/16" | 0.5625" | 14.288 mm |
| 5/8" | 0.625" | 15.875 mm |
| 11/16" | 0.6875" | 17.463 mm |
| 3/4" | 0.75" | 19.050 mm |
| 7/8" | 0.875" | 22.225 mm |
| 15/16" | 0.9375" | 23.813 mm |
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