DailyCalc

Decimal to Fraction Calculator

Turn any decimal, even a repeating one, into a fraction.

For a repeating decimal, put the repeating digits in brackets: 0.(3) or 0.1(6).

Answer

Try an example

Fraction

19/8

2.375 = 19/8 = 2 3/8.

Exact fraction
19/8
Mixed number
2 3/8
As a decimal
2.375

Fix the highlighted field to update the result.

Step by step

How the exact fraction was found
StepWorking
Write over a power of 103 decimal places, so 2.375 = 2375/1000
SimplifyGCD(2,375, 1,000) = 125, so the fraction is 19/8
Mixed number19 ÷ 8 = 2 remainder 3, so 2 3/8

How to use

  1. Type the decimal. For a repeating decimal, put the repeating digits in brackets: 0.(3) means 0.333… and 0.1(6) means 0.1666…
  2. Choose the answer you want: the exact fraction, the nearest 1/16 (or 1/8, 1/64…), or the simplest fraction with a denominator up to a limit.
  3. Read the fraction, the mixed number and the step-by-step working.

How decimal to fraction conversion works

Terminating decimals: write the digits over 10, 100, 1000 and so on, one zero per decimal place. Then divide the top and bottom by their greatest common divisor (GCD).

Repeating decimals: call the number x, multiply by a power of 10 to line up the repeating part, and subtract so the repeat cancels. Then solve for x.

Nearest fraction: for a ruler, multiply by 16 (or 8, 32, 64), round to a whole number, and put it over 16. The “simplest fraction” option instead finds the closest fraction whose denominator stays under your limit.

Examples

  • 2.375: 2375/1000, and the GCD is 125, so 19/8, or 2 3/8 as a mixed number.
  • 0.1(6): 100x = 16.(6) and 10x = 1.(6). Subtracting gives 90x = 15, so x = 15/90 = 1/6.
  • 3.(26): 100x − x = 326.(26) − 3.(26), so 99x = 323 and x = 323/99.
  • 0.3 inch to the nearest 1/16: 0.3 × 16 = 4.8, which rounds to 5, so about 5/16 inch (0.0125 too long).
  • 3.14159265358979 with denominators up to 1,000: the closest fraction is 355/113.

Common decimals as fractions

Decimal Fraction Nearest 1/16
0.125 1/8 1/8
0.2 1/5 3/16
0.25 1/4 1/4
0.3 3/10 5/16
0.(3) 1/3 5/16
0.375 3/8 3/8
0.5 1/2 1/2
0.625 5/8 5/8
0.(6) 2/3 11/16
0.75 3/4 3/4
0.875 7/8 7/8
0.333 versus 0.(3), and 0.999…

A decimal that stops is exact: 0.333 is 333/1000, not 1/3. Only the endlessly repeating 0.333… equals 1/3, so type it as 0.(3). The calculator suggests the bracket form when your digits look like a cut-off repeat.

A repeating 9 equals the next value up: 0.(9) = 1, because 10x − x = 9 gives x = 1.

To add or multiply the fractions you get, use the fraction calculator.

Frequently asked questions

How do I convert a decimal to a fraction?

Write the digits after the point over 10, 100, 1000 and so on (one zero per decimal place), then simplify. For example, 0.75 = 75/100 = 3/4.

How do I convert a repeating decimal to a fraction?

Multiply by 10 for each repeating digit, subtract the original number and solve. For x = 0.(3), 10x − x = 3, so 9x = 3 and x = 1/3.

Why is 0.333 not 1/3?

Because 0.333 stops after three digits, it is exactly 333/1000. Only 0.333… repeating forever equals 1/3. Type it as 0.(3), or use the nearest-fraction option.

How do I write a decimal in sixteenths of an inch?

Multiply by 16, round to the nearest whole number and put it over 16. For 0.3 inch: 0.3 × 16 = 4.8, which rounds to 5, giving about 5/16 inch.

Is 0.999… equal to 1?

Yes, 0.999… repeating is exactly 1. With x = 0.(9), 10x − x = 9, so 9x = 9 and x = 1.

How do I write a decimal as a mixed number?

Keep the whole-number part and convert only the decimal part. 2.375 = 2 + 375/1000 = 2 + 3/8, so the mixed number is 2 3/8.