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Fraction to Decimal Calculator

Convert a fraction or mixed number to a decimal with the repeating digits marked — 1/3 = 0.(3), 5/6 = 0.8(3) — rounded to any number of places, as a percent, with the long division worked out step by step.

Enter a mixed number

Whole number

Numerator (top)

Denominator (bottom)

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Show repeating digits as

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How it works

decimal = numerator ÷ denominator (long division) · percent = decimal × 100 the decimal terminates when the simplified denominator is 2ᵃ × 5ᵇ (after max(a, b) digits); otherwise a block of digits repeats, its length being the smallest k with 10ᵏ − 1 divisible by the rest of the denominator

A fraction bar is a division sign in disguise: 3/8 literally means 3 divided by 8. The calculator first simplifies the fraction, then looks at the prime factors of the denominator. If they are only 2s and 5s, the decimal terminates: 3/8 = 0.375, because 8 = 2³ and three digits are enough. Any other prime factor, such as 3, 7 or 11, makes the decimal repeat forever: 1/3 = 0.333… and 1/7 = 0.142857142857… The answer is shown exactly, with the repeating block marked in brackets, 0.(3) and 0.(142857), or with a bar or dots if you prefer. Some decimals start with digits that don’t repeat, as in 5/6 = 0.8(3). The steps work through the long division with your numbers, adding a 0 to each remainder until it reaches 0 or a remainder comes back. Once a remainder repeats, so do the digits. You can also round the result to the number of places you need, enter a mixed number such as 2 3/8, or use decimals in the numerator and denominator.

Worked example

3/8: 30 ÷ 8 = 3 remainder 6, 60 ÷ 8 = 7 remainder 4, 40 ÷ 8 = 5 remainder 0, so 3/8 = 0.375 exactly, or 37.5%. Multiplying the top and bottom by 125 gives the same result as 375/1000. 5/6 has a 3 in its denominator, so it repeats: 50 ÷ 6 = 8 remainder 2, then 20 ÷ 6 = 3 remainder 2 again and again, so 5/6 = 0.8(3) = 0.8333…, or 0.833 rounded to three places. The mixed number 2 1/7 is 15/7 = 2.(142857).

Sources: Repeating decimal — Wikipedia

Frequently asked questions

Which fractions give repeating decimals?

Simplify the fraction, then look at the denominator. If it has any prime factor other than 2 or 5 (like 3, 7 or 11), the decimal repeats: 1/3 = 0.(3) and 1/7 = 0.(142857). If it has only 2s and 5s, like 8, 20 or 125, the decimal ends.

What do the brackets in 0.8(3) mean?

The digits inside the brackets repeat forever, so 0.8(3) is 0.8333… with the 3 continuing without end. The same idea is often written with a bar over the repeating digits. Choose that style, or dots, under More options.

How long can the repeating block be?

Up to one less than the denominator. 1/7 repeats every 6 digits, 1/17 every 16 and 1/97 every 96. The calculator gives the length of the block and lists it in full up to 200 digits.

How exact is the decimal shown?

The main answer is exact: terminating decimals are shown in full, and repeating ones are written with their repeating block marked. The rounded value uses the number of places you choose.

How do I convert an improper fraction like 11/4 or a mixed number?

The same way: 11 ÷ 4 = 2.75. Improper just means the value is bigger than 1, so the decimal has a whole-number part. For a mixed number like 2 3/4, switch on the mixed-number box, or add the whole number to the decimal of the fraction: 2 + 0.75 = 2.75.