How it works
The numerator is divided by the denominator. If the division does not terminate, the result is shown to 12 significant figures rather than an endless string of digits.
Take 11/16 and divide by hand, one decimal place at a time. Carry the 11 forward to get 110; 16 goes into 110 six times with 14 left over, so the first digit is 6. The 14 carries forward to 140, which gives 8 with 12 left over. The 12 carries forward to 120, which gives 7 with 8 left over. The 8 carries forward to 80, which divides exactly into 5 and leaves nothing. Because the remainder reaches zero, 11/16 = 0.6875 exactly and no rounding is needed. Entering 22/32 instead returns the same 0.6875: only the value of the fraction matters, not the whole numbers used to write it.
This page converts a single fraction. Adding, subtracting, multiplying or dividing fractions is the Fraction Calculator; turning a decimal such as 0.4375 back into a fraction is the Decimal to Fraction Calculator. Results are tidied to 12 significant digits and shown with up to 10 decimal places, so 1/128 appears in full as 0.0078125 while 355/113 is rounded to 3.1415929204.
Formula: Decimal value = numerator ÷ denominator
Examples
A terminating decimal
3/4 = 3 ÷ 4 = 0.75.
A repeating decimal
1/3 = 1 ÷ 3 = 0.333333333333 (rounded).
A negative fraction
-7/8 = -7 ÷ 8 = -0.875 exactly. The sign belongs to the value, so the decimal carries it too, and a negative denominator behaves the same way: 3 ÷ -4 also gives -0.75.
Leading zeros after the decimal point
1/128 = 1 ÷ 128 = 0.0078125 exactly. The zeros are part of the value: multiplying 0.0078125 by 128 returns 1, while dropping them to read 0.78125 would multiply back to 100.
Common uses
- Converting a recipe quantity written as a fraction, such as 3/4 of a litre, into the decimal amount a scale or bottle label shows
- Checking a mark given as a fraction of the available marks against a decimal grade boundary
- Comparing two measurements written as fractions of the same unit, for example 3/8 inch against 0.375 inch
- Turning a fraction of an hour or of a kilometre into decimal units for a spreadsheet or a time record
Things to keep in mind
- The denominator cannot be zero.
- The numerator and the denominator must both be whole numbers. A decimal such as 2.5 in the numerator is rejected rather than rounded to 2, because rounding it quietly would change the value you asked about.
- Both numbers must sit inside the whole-number range that can be stored exactly, up to about 9,007,199,254,740,991. Anything larger is reported as too large to calculate exactly.
- A decimal terminates exactly only when the denominator, once the fraction has been reduced, has no prime factor other than 2 or 5. Since 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2, 1/128 stops at seven decimal places; 1/3 keeps a factor of 3 and repeats for ever, so its answer is rounded.
- The sign of the result follows the numerator, so a negative fraction gives a negative decimal, and a fraction of zero gives 0 rather than a negative zero.
- Only the division happens here. Taking a share of a larger quantity, such as 3/8 of 240, adds a multiplication step and belongs to the Fraction Calculator.
- For the wider relationship between the three notations, see the guide to fractions, decimals and percentages.