How to use the fraction to decimal converter
- Choose Fraction to decimal or Decimal to fraction.
- For a fraction, enter the numerator, the denominator and an optional whole number. For a decimal, type the decimal.
- For tape-measure work, choose Nearest 1/16 (or 1/8, 1/32, 1/64).
- Read the answer. A chart of inch fractions, with millimeters, is under the result.
Formula
Fraction to decimal: decimal = numerator / denominator (plus the whole number)
Decimal to fraction: write the decimal over 10, 100, 1000 and so on, then divide top and bottom by their greatest common divisor
Nearest 1/n: numerator = round(decimal part x n)
Repeating decimals are found by long division. The repeating block is shown in parentheses.
Worked examples
5/16 as a decimal: 5 divided by 16 is 0.3125, which ends, so it is exact.
1/3: the division never ends and repeats as 0.(3), meaning 0.3333...
2.75 as a fraction: 2.75 is 275/100. The greatest common divisor is 25, so it reduces to 11/4, which is the mixed number 2 3/4.
0.333 to the nearest 1/16: 0.333 x 16 = 5.33, which rounds to 5, so the answer is 5/16 (0.3125).
Which decimals end and which repeat?
A fraction in simplest form ends as a decimal only if its denominator has no prime factors other than 2 and 5. 3/8 ends (0.375). 1/7 repeats a six-digit block (0.(142857)).
Working with inches
Rulers and tape measures use halves, quarters, eighths, sixteenths and sometimes 32nds and 64ths. Choose a precision to round to the closest mark. The chart converts every 64th to decimal inches and millimeters (1 inch = 25.4 mm).
Common fractions to remember
1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875, 1/3 = 0.333..., 2/3 = 0.666... and 1/5 = 0.2. Knowing these makes it easy to estimate by eye before you check the exact answer here.
Assumptions and limits
- Whole numbers and numerators up to 1,000,000,000 are supported.
- Decimals can have up to 9 decimal places.
- Rounding to the nearest 1/n rounds halves up.
Frequently asked questions
How do I convert a fraction to a decimal?
Divide the top number by the bottom number. 3/4 is 3 / 4 = 0.75.
What is 0.625 as a fraction?
5/8. 0.625 is 625/1000, and dividing both by 125 gives 5/8.
How do I convert a mixed number?
Convert the fraction part and add the whole number. 2 3/4 is 2 + 0.75 = 2.75.
What fraction is 0.2?
1/5. 0.2 is 2/10, and dividing top and bottom by 2 gives 1/5.