Exact decimal value of any fraction, with the repeating block marked.
Quick examples
Example Result
1/4 = 0.25
Enter a fraction above and click Convert
Step 1 reduces the fraction by the greatest common divisor (GCD). Step 2 looks at the reduced denominator: only factors 2 and 5 means the decimal terminates; any other prime means it repeats. Step 3 is exact long division — divide, bring down a zero, record each remainder. Step 4: when a remainder comes back, the digits produced since its first appearance repeat forever. For 5/12 the remainder 8 returns, so 5/12 = 0.41(6).
Why the denominator decides: a terminating decimal is a fraction over 10, 100, 1000…, and powers of 10 contain only the primes 2 and 5. So 7/16 (16 = 2⁴) and 7/40 (40 = 2³ × 5) terminate, while 1/3, 5/12 and 1/7 repeat. This is why reducing first matters: 3/6 reduces to 1/2 = 0.5.
How many digits: for a terminating decimal, the number of decimal places is the larger of the powers of 2 and 5 in the reduced denominator (16 = 2⁴ → 4 places: 0.4375). For a repeating decimal the same count gives the digits before the cycle (12 = 2² × 3 → two: 0.41), and the cycle length depends on the remaining factor: 1/3 repeats every digit, 1/7 every 6, 1/97 every 96. For a prime denominator p the cycle length always divides p − 1.
| Symbol | Meaning |
|---|---|
| Numerator | Top number; a whole number, up to 30 digits |
| Denominator | Bottom number; a whole number other than 0 |
| GCD | Greatest common divisor, used to reduce the fraction first |
| 0.41(6) | Non-repeating digits, then the repeating block in brackets |
1A 7/16 in drill size.
16 = 2⁴ → four decimal places; 7 ÷ 16; × 25.4 for millimetres
7/16 = 0.4375 in = 11.1125 mm
Likewise 5/32 in = 0.15625 in = 3.96875 mm (1 inch is exactly 25.4 mm).
25/12, a repeating decimal with a non-repeating start.
12 = 2² × 3 → two digits before the cycle; 5 ÷ 12 = 0.41666…
5/12 = 0.41(6) ≈ 0.4167
Only the 6 repeats; the factor 3 in the denominator makes it repeat.
3Why 22/7 is not π.
22 ÷ 7 = 3.142857142857…; π = 3.14159265…
22/7 = 3.(142857)
The familiar approximation is too large from the third decimal place. 355/113 = 3.1415929… matches π to six decimal places — and its repeating block is 112 digits long.
The repeating block is marked with a bar on screen and with brackets when copied: 0.1(6) means 0.1666…, 0.(142857) means 0.142857142857….
The 20-place expansion writes the cycle out so you can copy a rounded value. Round to the precision you need: two decimals for money, three or four for inch measurements (7/16 in ≈ 0.438 in), more for engineering.
For the inverse, the Decimal to Fraction Calculator also rounds to the nearest 1/16, 1/32 or 1/64 inch.
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/2 | 0.5 | 1/3 | 0.(3) |
| 1/4 | 0.25 | 2/3 | 0.(6) |
| 3/4 | 0.75 | 1/6 | 0.1(6) |
| 1/8 | 0.125 | 5/6 | 0.8(3) |
| 3/8 | 0.375 | 1/7 | 0.(142857) |
| 5/8 | 0.625 | 1/9 | 0.(1) |
| 7/8 | 0.875 | 1/11 | 0.(09) |
| 1/16 | 0.0625 | 1/12 | 0.08(3) |