Quick answer
To convert a fraction to a decimal: divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75. If division ends, the decimal terminates. If a remainder repeats, the decimal is repeating (e.g. 1/3 = 0.333…).
How to use this calculator
Enter the numerator and denominator of any fraction. The calculator performs the division, identifies whether the result is terminating or repeating, shows the repeating block (if any), the percentage equivalent, and the simplified fraction.
Fraction to decimal formula
The conversion is simply division:
$$\text{Decimal} = \frac{\text{Numerator}}{\text{Denominator}}$$
$$\frac{3}{4} = 3 \div 4 = 0.75$$
Divide 3 by 4 using long division or a calculator. The quotient is the decimal equivalent.
Terminating decimals
A fraction produces a terminating decimal when — after simplifying to lowest terms — the denominator has only 2 and 5 as prime factors:
$$\frac{p}{q} \text{ terminates} \iff q \text{ has only factors of 2 and 5 after simplification}$$
| Denominator | Prime factors | Terminates? | Example |
|---|---|---|---|
| 2 | 2 | Yes | 1/2 = 0.5 |
| 4 | 2² | Yes | 3/4 = 0.75 |
| 5 | 5 | Yes | 2/5 = 0.4 |
| 8 | 2³ | Yes | 5/8 = 0.625 |
| 20 | 2² × 5 | Yes | 7/20 = 0.35 |
| 25 | 5² | Yes | 3/25 = 0.12 |
Repeating decimals
When the denominator (in lowest terms) contains a prime factor other than 2 or 5, the decimal repeats:
$$\frac{1}{3} = 0.\overline{3} = 0.333\ldots$$
| Denominator | Other prime factors | Example | Repeating block |
|---|---|---|---|
| 3 | 3 | 1/3 = 0.333… | 3 |
| 6 | 3 | 1/6 = 0.1666… | 6 |
| 7 | 7 | 1/7 = 0.142857142857… | 142857 |
| 9 | 3 | 1/9 = 0.111… | 1 |
| 11 | 11 | 1/11 = 0.0909… | 09 |
| 12 | 3 | 7/12 = 0.5833… | 3 |
Long division method
Long division traces the exact decimal digit by digit — and identifies repeating blocks when a remainder appears twice:
$$\frac{7}{12}: \quad 7 \div 12 = 0.58\overline{3}$$
7 ÷ 12: 7.000000 ÷ 12. Steps: 70 ÷ 12 = 5 rem 10 → 100 ÷ 12 = 8 rem 4 → 40 ÷ 12 = 3 rem 4 → remainder 4 repeats. Result: 0.583333… = 0.58̄3̄.
Worked examples
Example 1: 5/8 (terminating)
5 ÷ 8 = 0.625. GCD(5,8) = 1 — already simplified. Denominator 8 = 2³ → terminates. Percentage: 62.5%.
Example 2: 2/3 (repeating)
2 ÷ 3 = 0.666… = 0.6̄. Repeating block "6". Percentage: 66.666…% ≈ 66.67%.
Example 3: 7/6 (improper, mixed repeating)
7 ÷ 6 = 1.1666… = 1.16̄. Non-repeating part after decimal: "1"; repeating block: "6". As percentage: 116.67%.
Common fraction–decimal reference table
| Fraction | Decimal | Type | % |
|---|---|---|---|
| 1/2 | 0.5 | Terminating | 50% |
| 1/3 | 0.333… | Repeating | 33.3% |
| 1/4 | 0.25 | Terminating | 25% |
| 1/5 | 0.2 | Terminating | 20% |
| 1/6 | 0.1666… | Repeating | 16.7% |
| 1/7 | 0.142857… | Repeating (6-digit) | 14.29% |
| 1/8 | 0.125 | Terminating | 12.5% |
| 2/3 | 0.666… | Repeating | 66.7% |
| 3/4 | 0.75 | Terminating | 75% |
| 5/6 | 0.8333… | Repeating | 83.3% |
| 7/8 | 0.875 | Terminating | 87.5% |
Common mistakes
Rounding a repeating decimal
1/3 ≈ 0.33 is an approximation. The exact value is 0.333… If you need an exact result in calculations, keep it as a fraction.
Thinking all decimals terminate
Only fractions whose denominator (in lowest terms) has no prime factors other than 2 and 5 will produce a terminating decimal. 1/3, 1/6, 1/7 are all repeating.
Frequently asked questions
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. The quotient is the decimal. If a remainder repeats, the decimal is repeating.
What is 1/3 as a decimal?
0.333… = 0.3̄ (repeating). It is not possible to express 1/3 as a finite decimal.
How do you know if a fraction gives a terminating or repeating decimal?
Simplify the fraction. If the denominator's prime factors are only 2 and 5, it terminates. Any other prime factor (3, 7, 11…) causes repetition.
What is 5/8 as a decimal?
0.625. Since 8 = 2³, the decimal terminates exactly.