About the Decimal to Fraction Calculator
This decimal to fraction calculator converts a decimal such as 0.625 into its exact simplified fraction (5/8), a mixed number and a percentage. It also works in reverse: type a fraction like 7/12 and it returns the decimal, marking the repeating part in brackets — 0.58(3).
Repeating decimals are supported directly. Put the repeating digits in parentheses, so 0.(3) means 0.333… and 1.1(6) means 1.1666…, and the calculator returns the exact fraction (1/3 and 7/6) rather than a rounded approximation. That makes it handy for algebra homework and for checking calculator output.
For workshop, sewing and cooking measurements it also shows the nearest fraction with a denominator of your choice — the closest 1/16 or 1/64 of an inch, for example — so you can read the value straight off a tape measure or measuring cup.
How to use the decimal to fraction calculator
- 1Type a decimal (0.875), a repeating decimal with brackets (0.(45)) or a fraction (5/16).
- 2Read the simplified fraction and mixed number.
- 3Check the exact decimal to see any repeating digits.
- 4Choose a denominator such as 1/16 to get the nearest tape-measure fraction.
Formula and method
A terminating decimal with k digits after the point is that digit string over 10ᵏ — 0.625 is 625/1000. The fraction is then simplified by dividing the numerator and denominator by their greatest common factor (125), giving 5/8.
For a repeating decimal I.A(B), where A is the non-repeating block of a digits and B the repeating block of b digits, subtract the number written without the repeat from the number written with one copy of it, and divide by 10ᵃ × (10ᵇ − 1). For 1.1(6): (116 − 11) ÷ (10 × 9) = 105/90 = 7/6. The nearest measuring fraction rounds the value to the closest multiple of 1/denominator (for example the nearest 1/16 of an inch) and then reduces it.
- k
- Number of digits after the decimal point
- A, a
- Non-repeating digits after the point and how many there are
- B, b
- Repeating digits and how many there are
Worked examples
0.625 as a fraction
0.625 = 625/1000. The greatest common factor of 625 and 1000 is 125, so it simplifies to 5/8, which is also exactly 10/16 of an inch.
Repeating decimal 0.333…
With one repeating digit and no non-repeating digits, the fraction is 3 ÷ 9 = 1/3.
1.1666… (1.1 with 6 repeating)
Using (116 − 11) ÷ (10 × 9) = 105/90, which simplifies to 7/6, or 1 1/6 as a mixed number.
Fraction to decimal: 7/12
Dividing 7 by 12 gives 0.58333…, where the 3 repeats forever, written 0.58(3).
2.375 inches
2.375 = 2375/1000 = 19/8, which reads as 2 3/8 inches on a tape measure.
0.3 inch to the nearest 1/16
0.3 is exactly 3/10, which is not on a 1/16 scale. 0.3 × 16 = 4.8, which rounds to 5, so the closest tape-measure mark is 5/16 (0.3125), 0.0125 in too long.
Frequently asked questions
How do you 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. 0.45 becomes 45/100, and dividing by 5 gives 9/20.
How do you convert a repeating decimal to a fraction?+
For a pure repeat, put the repeating block over as many 9s as it has digits: 0.(27) = 27/99 = 3/11. If some digits come before the repeat, use (whole number with repeat − number without repeat) ÷ (9s followed by 0s).
What is 0.3 repeating as a fraction?+
0.333… equals exactly 1/3. Likewise 0.666… is 2/3 and 0.999… is exactly 1, because 9/9 = 1.
How do I convert a fraction to a decimal?+
Divide the numerator by the denominator. If the simplified denominator has only 2s and 5s as prime factors the decimal ends (3/8 = 0.375); otherwise it repeats (5/6 = 0.8333…).
What is 0.125 as a fraction?+
0.125 = 125/1000, which simplifies to 1/8. Other common ones: 0.25 = 1/4, 0.375 = 3/8, 0.5 = 1/2, 0.625 = 5/8, 0.75 = 3/4 and 0.875 = 7/8.