Fraction Converter: Fraction to Decimal, Percent and Simplest Form
Fractions ↔ decimals ↔ percentages, simplified. Free, no sign-up.
Fraction → decimal, %, simplified
Decimal (6 places)
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Exact (recurring)
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Percent
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Simplified
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Mixed
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Decimal → fraction (recurring decimals too)
Type a decimal such as 0.75, or put the repeating digits in brackets: 0.(3) = 0.333…, 0.1(6) = 0.1666…
Fraction: —
How to use the fraction converter
- Enter a numerator and denominator in the first card. Negative numbers and decimals (such as 2.5/7.5) are accepted.
- Read the decimal, the exact decimal with its repeating block in brackets, the percentage, the simplest form and the mixed number.
- To go the other way, type a decimal in the second card. For a recurring decimal, put the repeating digits in brackets, for example
0.(142857)for 1/7. - All results update as you type, and every simplification is exact.
How the conversions work
Fraction to percent
Percent = (Numerator ÷ Denominator) × 100
Example: 7/8 = 0.875 = 87.5%. A UPSC mock score of 147/200 is 73.5%.
Recurring decimal to fraction
0.a(b) = (ab − a) ÷ (9 followed by 0s): 0.1(6) = (16 − 1) ÷ 90 = 1/6
Use one 9 for each repeating digit and one 0 for each non-repeating digit after the decimal point.
Common fraction, decimal and percent equivalents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/3 | 0.(3) | 33.33% |
| 1/6 | 0.1(6) | 16.67% |
| 1/7 | 0.(142857) | 14.29% |
| 1/8 | 0.125 | 12.5% |
| 1/9 | 0.(1) | 11.11% |
| 1/11 | 0.(09) | 9.09% |
| 1/12 | 0.08(3) | 8.33% |
Tips for CSAT and SSC arithmetic
- Learn the sevenths: 1/7 = 0.142857…, and 2/7, 3/7 and so on use the same six digits in rotation (2/7 = 0.285714…).
- Compare fractions by cross-multiplying instead of converting: 5/8 vs 7/11 → 55 vs 56, so 7/11 is larger.
- Use the terminating rule (denominator with only 2s and 5s) to rule out options quickly.
Common mistakes
- Writing 0.333 as 1/3. It is 333/1000; only the recurring 0.(3) equals 1/3.
- Forgetting to simplify fully. Always divide by the HCF, not just by 2.
- Placing the minus sign in the denominator. The convention is −3/4, not 3/−4.
Key facts
- Every fraction of whole numbers is either a terminating or a recurring decimal.
- 0.(9) is exactly equal to 1.
- The repeating block of 1/n has at most n − 1 digits.
Frequently asked questions
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75, and 1/8 = 0.125.
How do I simplify a fraction?
Divide the numerator and denominator by their HCF (greatest common divisor). For example, 18/24 has HCF 6, so it simplifies to 3/4.
How do I convert a decimal to a fraction?
Write the decimal over a power of 10 with as many zeros as there are decimal places, then simplify. For example, 0.375 = 375/1000 = 3/8.
How do I convert a recurring decimal to a fraction?
Put the repeating digits over the same number of 9s. 0.(3) = 3/9 = 1/3 and 0.(27) = 27/99 = 3/11. For 0.1(6), subtract the non-repeating part: (16 − 1)/90 = 15/90 = 1/6.
Which fractions give terminating decimals?
A fraction in its simplest form terminates only when its denominator has no prime factors other than 2 and 5. So 3/40 terminates (0.075), but 1/6 and 1/7 recur.
What is a mixed number?
A mixed number is a whole number plus a proper fraction, such as 2 1/2, which equals 5/2 or 2.5. To convert an improper fraction, divide: 17/5 = 3 remainder 2, so 3 2/5.