Fraction to Decimal Calculator
Type a fraction or mixed number to get its decimal, worked out by long division, with any repeating digits marked.
5/12 as a decimal
0.416
5/12 = 0.416667… as a decimal; the block 6 repeats for ever.
- Rounded to 4 places
- 0.4167
- As a percentage
- ≈ 41.6667%
- Why it repeats
- denominator has a factor of 3
How this works: Method, 2 sources, Checked against 2 worked examples,
How this works
Method
A fraction is a division: 5/12 means 5 ÷ 12. Long division gives the decimal one digit at a time. 12 doesn’t go into 5, so write 0 and a decimal point, bring down a zero to make 50, and 12 goes in 4 times with 2 left. Bring down another zero: 20 ÷ 12 = 1 remainder 8. Then 80 ÷ 12 = 6 remainder 8, and the remainder 8 keeps coming back, so the 6 repeats for ever: 5/12 = 0.41666… Full method
Sources
How it’s tested
2 worked examples for this page are checked by automated tests before every release: given the inputs, the tool must show the expected answer.
Privacy
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Changes
- First published, with nine pages: adding, subtracting, multiplying, dividing and simplifying fractions, fraction to decimal and back, mixed numbers and ratios.
How to convert a fraction to a decimal
A fraction is a division: 5/12 means 5 ÷ 12. Long division gives the decimal one digit at a time. 12 doesn’t go into 5, so write 0 and a decimal point, bring down a zero to make 50, and 12 goes in 4 times with 2 left. Bring down another zero: 20 ÷ 12 = 1 remainder 8. Then 80 ÷ 12 = 6 remainder 8, and the remainder 8 keeps coming back, so the 6 repeats for ever: 5/12 = 0.41666…
Every fraction either ends or repeats, because there are only so many possible remainders (fewer than the denominator); as soon as one comes back, the digits cycle. Whether it ends depends only on the denominator in lowest terms: it terminates exactly when the denominator’s only prime factors are 2 and 5, the factors of 10.
Repeating digits are written with a bar over them (0.41 6̅) or, where a bar can’t be typed, in brackets: 0.41(6). The repeating block can be long; 1/7 = 0.142857 142857 …, a block of six digits.
a/b = a ÷ b; terminates ⇔ b (in lowest terms) = 2ᵐ × 5ⁿ
- Grade 7 standards ask students to convert a rational number to a decimal using long division and to know that its decimal form terminates in 0s or eventually repeats (7.NS.A.2d). Source: Common Core State Standards, Grade 7 The Number System (7.NS.A.2d).
- The repeating block of 1/p for a prime p (other than 2 and 5) has a length that divides p − 1; for 1/7 it is the full 6 digits. Source: Wikipedia, Repeating decimal.
Fractions as decimals
Exact decimals; a block in brackets repeats for ever.
| Fraction | Decimal | Ends or repeats | Percent |
|---|---|---|---|
| 1/2 | 0.5 | ends | 50% |
| 1/3 | 0.(3) | repeats | 33.33% |
| 2/3 | 0.(6) | repeats | 66.67% |
| 1/4 | 0.25 | ends | 25% |
| 3/4 | 0.75 | ends | 75% |
| 1/5 | 0.2 | ends | 20% |
| 1/6 | 0.1(6) | repeats | 16.67% |
| 5/6 | 0.8(3) | repeats | 83.33% |
| 1/7 | 0.(142857) | repeats | 14.29% |
| 1/8 | 0.125 | ends | 12.5% |
Show all 22 rowsShow fewer
| 3/8 | 0.375 | ends | 37.5% |
| 5/8 | 0.625 | ends | 62.5% |
| 7/8 | 0.875 | ends | 87.5% |
| 1/9 | 0.(1) | repeats | 11.11% |
| 1/10 | 0.1 | ends | 10% |
| 1/11 | 0.(09) | repeats | 9.09% |
| 1/12 | 0.08(3) | repeats | 8.33% |
| 5/12 | 0.41(6) | repeats | 41.67% |
| 1/16 | 0.0625 | ends | 6.25% |
| 1/20 | 0.05 | ends | 5% |
| 3/40 | 0.075 | ends | 7.5% |
| 1/13 | 0.(076923) | repeats | 7.69% |
Frequently Asked Questions
How do I turn a fraction into a decimal without a calculator?
Divide the numerator by the denominator by long division, adding zeros after the decimal point as you go. Or, if the denominator divides into 10, 100 or 1,000, scale it up: 3/25 = 12/100 = 0.12.
Why does 1/3 never end?
Every step of 1 ÷ 3 leaves remainder 1, so you bring down 10 and get 3 again, for ever. 3 is not a factor of any power of 10, so no number of decimal places can hold 1/3 exactly.
What is 3/8 as a decimal?
0.375. Because 8 = 2³, the decimal ends after three places: 3/8 = 375/1000.