Fraction to Decimal Calculator
Every fraction is a division problem: the top divided by the bottom. The calculator does the long division for you, digit by digit, and stops as soon as it spots a repeating pattern.
Answer
The block “6” repeats forever · ≈ 0.41666667
Step by step
- A fraction means division: 5/12 = 5 ÷ 12.
- 5 ÷ 12 = 0 remainder 5.
- Bring down a 0: 50 ÷ 12 = 4 remainder 2.
- Bring down a 0: 20 ÷ 12 = 1 remainder 8.
- Bring down a 0: 80 ÷ 12 = 6 remainder 8.
- Remainder 8 has appeared before, so the digits “6” repeat forever.
Answer: 0.416̅
Still stuck? Ask the tutor about these steps
How it works
a/b = a ÷ bDivide the numerator by the denominator. When the numerator is smaller, write 0. and bring down zeros.
The decimal stops (terminates) if the simplified denominator has no prime factors other than 2 and 5 — like 8, 20 or 125.
Any other denominator gives a repeating decimal. The digits start repeating as soon as a remainder comes up for the second time, and a bar is drawn over the repeating block.
Worked example
Convert 5/12 to a decimal.
- 5 ÷ 12 = 0 remainder 5
- 50 ÷ 12 = 4 r 2 · 20 ÷ 12 = 1 r 8 · 80 ÷ 12 = 6 r 8
- Remainder 8 repeats → 0.416̅
Common fractions, decimals and percents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3̅ | 33.3̅% |
| 2/3 | 0.6̅ | 66.6̅% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 4/5 | 0.8 | 80% |
| 1/6 | 0.16̅ | 16.6̅% |
| 5/6 | 0.83̅ | 83.3̅% |
| 1/7 | 0.1̅4̅2̅8̅5̅7̅ | 14.2̅8̅5̅7̅1̅4̅% |
| 2/7 | 0.2̅8̅5̅7̅1̅4̅ | 28.5̅7̅1̅4̅2̅8̅% |
| 3/7 | 0.4̅2̅8̅5̅7̅1̅ | 42.8̅5̅7̅1̅4̅2̅% |
| 4/7 | 0.5̅7̅1̅4̅2̅8̅ | 57.1̅4̅2̅8̅5̅7̅% |
| 5/7 | 0.7̅1̅4̅2̅8̅5̅ | 71.4̅2̅8̅5̅7̅1̅% |
| 6/7 | 0.8̅5̅7̅1̅4̅2̅ | 85.7̅1̅4̅2̅8̅5̅% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/9 | 0.1̅ | 11.1̅% |
| 2/9 | 0.2̅ | 22.2̅% |
| 4/9 | 0.4̅ | 44.4̅% |
| 5/9 | 0.5̅ | 55.5̅% |
| 7/9 | 0.7̅ | 77.7̅% |
| 8/9 | 0.8̅ | 88.8̅% |
| 1/10 | 0.1 | 10% |
| 3/10 | 0.3 | 30% |
| 7/10 | 0.7 | 70% |
| 9/10 | 0.9 | 90% |
| 1/11 | 0.0̅9̅ | 9.0̅9̅% |
| 2/11 | 0.1̅8̅ | 18.1̅8̅% |
| 3/11 | 0.2̅7̅ | 27.2̅7̅% |
| 4/11 | 0.3̅6̅ | 36.3̅6̅% |
| 5/11 | 0.4̅5̅ | 45.4̅5̅% |
| 6/11 | 0.5̅4̅ | 54.5̅4̅% |
| 7/11 | 0.6̅3̅ | 63.6̅3̅% |
| 8/11 | 0.7̅2̅ | 72.7̅2̅% |
| 9/11 | 0.8̅1̅ | 81.8̅1̅% |
| 10/11 | 0.9̅0̅ | 90.9̅0̅% |
| 1/12 | 0.083̅ | 8.3̅% |
| 5/12 | 0.416̅ | 41.6̅% |
| 7/12 | 0.583̅ | 58.3̅% |
| 11/12 | 0.916̅ | 91.6̅% |
A bar over digits means they repeat forever: 0.3̅ = 0.333…
Frequently asked questions
How do you turn a fraction into a decimal?
Divide the top number by the bottom number. 3/8 = 3 ÷ 8 = 0.375.
How can I tell if a decimal will repeat?
Simplify the fraction and look at the denominator. If its only prime factors are 2s and 5s the decimal ends; otherwise it repeats.
What is 1/3 as a decimal?
0.333… with the 3 repeating forever, written 0.3̅.