How to use the decimal to fraction calculator
Type one number with a period as the decimal point. Plain entries like 0.125, .625, -2.4 or 7 are read exactly as written. If some digits repeat forever, put only the repeating part in parentheses: 0.(3) means 0.333... and 1.2(34) means 1.2343434...
The big answer is the simplified fraction. Below it you'll find the starting fraction, the GCF that reduced it, the mixed number, the decimal and percentage forms, whether the fraction's decimal ends or repeats, and a table of equivalent fractions.
- Type the decimal, with the minus sign first if it's negative. Leave out thousands commas.
- For a repeating decimal, wrap just the repeating digits in parentheses, like 0.1(6).
- Press Convert to fraction.
- Read the simplified fraction, then the mixed number if the value is more than 1.
- Use the starting fraction and GCF rows to follow or check the reduction.
Decimal to fraction chart in sixteenths
Every step of 0.0625 is one more sixteenth. Use it with any ruler or tape measure marked in sixteenths of an inch. Each fraction is shown in lowest terms.
| Decimal | Fraction | In sixteenths |
|---|---|---|
| 0.0625 | 1/16 | 1/16 |
| 0.125 | 1/8 | 2/16 |
| 0.1875 | 3/16 | 3/16 |
| 0.25 | 1/4 | 4/16 |
| 0.3125 | 5/16 | 5/16 |
| 0.375 | 3/8 | 6/16 |
| 0.4375 | 7/16 | 7/16 |
| 0.5 | 1/2 | 8/16 |
| 0.5625 | 9/16 | 9/16 |
| 0.625 | 5/8 | 10/16 |
| 0.6875 | 11/16 | 11/16 |
| 0.75 | 3/4 | 12/16 |
| 0.8125 | 13/16 | 13/16 |
| 0.875 | 7/8 | 14/16 |
| 0.9375 | 15/16 | 15/16 |
| 1 | 1 | 16/16 |
Common decimals as fractions
Tenths and the usual repeating decimals don't land on a sixteenth, so they get their own chart. The repeating rows use the same parentheses you'd type into the converter. Note that 0.33 and 0.(3) are different numbers: 0.33 is exactly 33/100.
| Decimal | Fraction | Type |
|---|---|---|
| 0.1 | 1/10 | Terminating |
| 0.2 | 1/5 | Terminating |
| 0.25 | 1/4 | Terminating |
| 0.3 | 3/10 | Terminating |
| 0.4 | 2/5 | Terminating |
| 0.6 | 3/5 | Terminating |
| 0.7 | 7/10 | Terminating |
| 0.75 | 3/4 | Terminating |
| 0.8 | 4/5 | Terminating |
| 0.9 | 9/10 | Terminating |
| 0.111... = 0.(1) | 1/9 | Repeating |
| 0.1666... = 0.1(6) | 1/6 | Repeating |
| 0.333... = 0.(3) | 1/3 | Repeating |
| 0.666... = 0.(6) | 2/3 | Repeating |
| 0.8333... = 0.8(3) | 5/6 | Repeating |
The place value method for decimals that end
A decimal that stops is already a fraction in disguise. Tenths sit over 10, hundredths over 100, thousandths over 1,000. Count the digits after the point, drop the point, and put that whole number over 1 followed by that many zeros. Then divide top and bottom by their greatest common factor.
For 3.2117, four places give 32117/10000, which doesn't reduce. For 0.125, three places give 125/1000. The GCF is 125, so the answer is 1/8. Extra zeros on the end, like 0.1250, make a bigger starting fraction but reduce to the same answer.
Fraction = digits without the decimal point / 10^n, where n is the number of decimal placesLowest terms: divide the numerator and denominator by GCF(numerator, denominator)
Repeating decimal to fraction
When a block of digits repeats forever, the place value method can't work because there's no last digit. Instead, the repeat goes over a run of 9s. A one-digit repeat goes over 9, a two-digit repeat over 99, so 0.(27) = 27/99 = 3/11.
If some digits come before the repeat, take the digits through one full repeat, subtract the digits before the repeat, and divide by the matching 9s followed by 0s. For 1.2(34), that's (1234 - 12) / 990 = 1222/990. Dividing by 2 gives 611/495, or 1 116/495 as a mixed number.
Pure repeat: 0.(R) = R / (10^r - 1), where r is the number of repeating digitsDelayed repeat: (digits through one repeat - digits before the repeat) / (10^(m+r) - 10^m), where m digits come before the repeat
Decimal to fraction inches
A drawing that says 2.375 in converts cleanly: 0.375 is 3/8, so it's 2 3/8 inches on the tape. Any decimal from the sixteenths chart above lands exactly on a ruler mark.
Most decimals don't. The converter gives the exact fraction, so 0.3 in comes out as 3/10, which isn't on a tape. To find the nearest sixteenth, multiply the decimal by 16, round to a whole number and put it over 16. For 0.3, that's 4.8, which rounds to 5, so 5/16 in (0.3125 in, which is 0.0125 in longer). For 0.65, 10.4 rounds to 10, and 10/16 reduces to 5/8 in.
Nearest sixteenth = round(decimal inches x 16) / 16
Worked examples
These cover a plain decimal, a negative number, a whole number written with decimals, and three kinds of repeat. Each one matches what the converter shows in its starting fraction and GCF rows.
| You type | Starting fraction | Divide by | Answer |
|---|---|---|---|
| 0.125 | 125/1000 | 125 | 1/8 |
| -2.4 | -24/10 | 2 | -12/5 = -2 2/5 |
| 6.000 | 6000/1000 | 1000 | 6 |
| 0.(27) | 27/99 | 9 | 3/11 |
| 0.1(6) | 15/90 | 15 | 1/6 |
| 1.2(34) | 1222/990 | 2 | 611/495 |
When the decimal was rounded
The converter treats what you type as exact. If a screen showed 0.333 after rounding, you'll get 333/1000, because nothing in those digits says the 3s keep going. Type 0.(3) only when you know the value really is one third.
The same goes for measurements. Turning 0.3 in into 5/16 in is a rounding choice, and it's off by 0.0125 in. That's fine for framing and too loose for machining, so keep the tolerance of the job in mind before you swap a decimal for a handy fraction.
Sources
These references cover the place value method, the repeating decimal method and the rule for which fractions end in base 10.