Common Decimal-Fraction Equivalents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 2/3 | 0.666... | 66.67% |
| 3/4 | 0.75 | 75% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
The Conversion Method
Decimal to Fraction: Count decimal places. Write the number without the decimal point over 10^(number of places). Simplify. 0.375 has 3 decimal places → 375/1000. GCD of 375 and 1000 is 125 → 375÷125 / 1000÷125 = 3/8.
Fraction to Decimal: Divide numerator by denominator. 7/8 = 7 ÷ 8 = 0.875. Some fractions produce repeating decimals: 1/3 = 0.333..., 1/7 = 0.142857142857...
When Do Fractions Terminate?
A fraction in lowest terms produces a terminating decimal only if the denominator's prime factors are all 2s and 5s. That's why 1/8 (denominator = 2³) terminates at 0.125, but 1/3 (denominator = 3) repeats. 1/6 (denominator = 2×3) repeats because of the factor of 3.