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…).
- One operation only: numerator ÷ denominator. No special steps needed - just division.
- Test before you divide: simplify the fraction, then check the denominator's prime factors. Only 2s and 5s? Terminates. Anything else? Repeats.
- Always simplify first. 6/9 = 2/3 (repeating). 6/10 = 3/5 (terminating). The unsimplified denominator can give the wrong answer to the terminate-or-repeat test.
- Repeating decimals are exact, not approximate. 0.333… = 1/3 precisely. Rounding to 0.33 introduces error; keeping the fraction keeps the truth.
- 1/7 has the longest common repeating block: 142857 (6 digits), longer than any other single-digit denominator.
How to use this fraction to decimal 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.
Fraction to decimal explained to a beginner
Think of converting a fraction as making change from a dollar. A dollar has 100 cents - a clean base-10 grid. 1/4 = exactly 25 cents. Done, no remainder. But 1/3 = 33.333... cents - there is no exact number of cents that equals a third, so the digits keep going forever.
This is why the "only 2 and 5 as prime factors" rule works. Our number system is base-10, and 10 = 2 × 5. Any denominator built only from 2s and 5s will divide cleanly into some power of 10 (10, 100, 1000...). So the decimal always stops. Any other prime - 3, 7, 11 - never divides cleanly into any power of 10, so the decimal never stops.
In other words: the denominator tells you whether clean change is possible before you even start dividing.
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 |
The 1/7 row is worth a second look. Six digits repeat before the cycle closes - longer than any other single-digit denominator. When people do long division by hand and expect a pattern to appear in one or two steps, 1/7 consistently surprises them.
You need to carry the division through six full remainders before seeing the same remainder twice, which signals where the cycle ends.
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 for calculation
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
The table below covers the 11 fractions that appear most often in everyday arithmetic - from cooking and construction to finance.
The Type column tells you whether the decimal is exact (terminating) or goes on forever (repeating). Memorizing the terminating ones (1/2, 1/4, 1/5, 1/8, 3/4, 7/8) is worth it: they come up constantly and save you a calculation.
| 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 when converting fraction to decimal
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.
In any multi-step calculation, I keep repeating decimals in fraction form rather than converting early. If you substitute 0.33 for 1/3 and that value feeds into several further operations, each step carries forward a small error.
Fractions preserve the exact value through every step without accumulation - convert to decimal only as the final output.
FAQs about fraction to decimal calculation
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.
Quiz: how well do you know fraction to decimal?
1. How do you convert a fraction to its decimal equivalent?
2. What is 5/8 as a decimal?
3. After simplifying a fraction, what does it mean if the denominator contains a prime factor other than 2 or 5?
4. According to the reference table on this page, which fraction has a repeating decimal with a 6-digit repeating block?
5. A student tests 3/6 by checking the denominator 6, which contains the factor 3. They conclude the decimal repeats. But 3/6 = 0.5 exactly. What rule did they skip?