OneTaskBy Tim King · Updated
Fraction to Decimal Calculator
Mixed Numbers to Decimals and Percentages, With Repeating Digits Marked
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How the Fraction to Decimal Calculator works
This fraction to decimal calculator divides the top of a fraction by the bottom and gives the exact decimal, with any repeating block found and shown in brackets. Add a whole number to convert a mixed number such as 2 1/3. It also gives the percentage and says whether the decimal ends.
A fraction is a division waiting to happen: 3/8 means 3 ÷ 8. Doing that division gives the decimal. Some fractions stop after a few digits, and others settle into a block of digits that repeats for ever, such as 1/3 = 0.333… or 1/7 = 0.142857142857…
How the fraction to decimal calculator works
The formula is decimal = numerator ÷ denominator. For a mixed number the whole part is folded in first: w a/b = (w × b + a) ÷ b. The calculator divides digit by digit and keeps track of every remainder. If a remainder comes back, the digits from that point repeat, and the block is shown in brackets. Whether a fraction repeats depends only on its denominator in lowest terms: if its prime factors are only 2s and 5s, the decimal ends.
First example. 3/8 is 3 ÷ 8 = 0.375. Eight is 2 × 2 × 2, so the decimal ends after three places.
Second example. 5/12 is 0.41666… and the 6 repeats, written 0.41(6). Twelve is 2 × 2 × 3, and the 3 is what makes it repeat.
How many hours is 2 3/4 hours in decimal? (2 × 4 + 3) ÷ 4 = 11 ÷ 4 = 2.75 hours.
Every fraction from 1/12 to 11/12 as a decimal and a percentage; brackets mark repeating digits
| Fraction | Simplest form | Decimal | Percentage |
|---|---|---|---|
| 1/12 | 0.08(3) | 8.333333% | |
| 2/12 | 1/6 | 0.1(6) | 16.666667% |
| 3/12 | 1/4 | 0.25 | 25% |
| 4/12 | 1/3 | 0.(3) | 33.333333% |
| 5/12 | 0.41(6) | 41.666667% | |
| 6/12 | 1/2 | 0.5 | 50% |
| 7/12 | 0.58(3) | 58.333333% | |
| 8/12 | 2/3 | 0.(6) | 66.666667% |
| 9/12 | 3/4 | 0.75 | 75% |
| 10/12 | 5/6 | 0.8(3) | 83.333333% |
| 11/12 | 0.91(6) | 91.666667% |
Fractions that give repeating decimals, with brackets around the digits that repeat
| Fraction | Decimal | Repeating block length | Percentage |
|---|---|---|---|
| 1/3 | 0.(3) | 1 | 33.33% |
| 2/3 | 0.(6) | 1 | 66.67% |
| 1/6 | 0.1(6) | 1 | 16.67% |
| 5/6 | 0.8(3) | 1 | 83.33% |
| 1/7 | 0.(142857) | 6 | 14.29% |
| 2/7 | 0.(285714) | 6 | 28.57% |
| 3/7 | 0.(428571) | 6 | 42.86% |
| 4/7 | 0.(571428) | 6 | 57.14% |
| 5/7 | 0.(714285) | 6 | 71.43% |
| 6/7 | 0.(857142) | 6 | 85.71% |
| 1/9 | 0.(1) | 1 | 11.11% |
| 2/9 | 0.(2) | 1 | 22.22% |
| 4/9 | 0.(4) | 1 | 44.44% |
| 5/9 | 0.(5) | 1 | 55.56% |
| 7/9 | 0.(7) | 1 | 77.78% |
| 8/9 | 0.(8) | 1 | 88.89% |
| 1/11 | 0.(09) | 2 | 9.09% |
| 2/11 | 0.(18) | 2 | 18.18% |
| 3/11 | 0.(27) | 2 | 27.27% |
| 4/11 | 0.(36) | 2 | 36.36% |
| 5/11 | 0.(45) | 2 | 45.45% |
| 6/11 | 0.(54) | 2 | 54.55% |
| 7/11 | 0.(63) | 2 | 63.64% |
| 8/11 | 0.(72) | 2 | 72.73% |
| 9/11 | 0.(81) | 2 | 81.82% |
| 10/11 | 0.(90) | 2 | 90.91% |
Tips
- Use the lowest terms to predict. 3/12 ends because it is really 1/4.
- Bar notation. 0.41(6) is the same as 0.416 with a bar over the 6.
- Rounding for money. Round to two places only at the end, not halfway through.
FAQ
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. 7/8 is 7 ÷ 8 = 0.875. If you are doing it by hand, use long division: put a decimal point after the 7, add zeros, and keep dividing until the remainder is 0 or a remainder repeats. A calculator or this page does the same steps instantly.
Which fractions make repeating decimals?
Put the fraction in lowest terms and look at the denominator. If it has any prime factor other than 2 or 5, such as 3, 7, 11 or 13, the decimal repeats. So 1/3, 2/9, 5/6 and 4/7 repeat, while 1/4, 3/20 and 7/40 end. The number of decimal places in an ending decimal is never more than the larger power of 2 or 5.
What is 1/3 as a decimal?
1/3 is 0.333… with the 3 repeating for ever, written 0.(3) or 0.3 with a bar over it. Rounded to two places it is 0.33, and as a percentage it is 33.33…%, often written 33 1/3%. Two thirds is 0.666…, which rounds to 0.67.
How do you convert a mixed number to a decimal?
Keep the whole number and convert only the fraction part, then put them together: 3 2/5 is 3 + 0.4 = 3.4. Or turn it into an improper fraction first, (3 × 5 + 2)/5 = 17/5, and divide. Enter the whole number in the first box and the calculator does the folding for you.
See also: all Arithmetic tools, Number Theory, Algebra and Geometry, Statistics, Trigonometry and Calculus.
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