Fraction to Decimal Calculator — Exact & Repeating

Long division, 5 ÷ 7
Bring down	÷ 7	Remainder
50	7	1
10	1	3
30	4	2
20	2	6
60	8	4
40	5	5

Long division, 5 ÷ 7

Bring down

÷ 7

Remainder

How to convert a fraction to a decimal

A fraction is a division: the numerator divided by the denominator. To do it by hand, use long division and keep bringing down zeros:

Step	Bring down	÷ 8	Remainder
1	30	3	6
2	60	7	4
3	40	5	0

The digits 3, 7, 5 give 3/8 = 0.375, and the remainder 0 means the decimal ends. For a mixed number such as 2 1/6, write it as an improper fraction (13/6) or convert just the fraction part and add the whole number. The calculator shows the same table for any fraction you enter, along with the simplest form of the fraction itself.

Decimals that end and decimals that repeat

When a remainder comes back that has already appeared, the digits from that point repeat forever. Dividing 5 by 7 gives the remainders 1, 3, 2, 6, 4, 5 and then 1 again, so the six digits 714285 repeat: 0.714285714285…. Whether a fraction ends or repeats depends only on its denominator in lowest terms: if it has no prime factors other than 2 and 5 — like 4, 8, 20 or 125 — the decimal ends; any other prime, such as 3 in 1/6 or 7 in 5/7, makes it repeat. The result says which kind you have and why.

Writing repeating decimals

The standard notation is a bar over the repeating digits: 1/3 = 0.3̅, 1/6 = 0.16̅, 5/7 = 0.7̅1̅4̅2̅8̅5̅. In computer input and some textbooks the same block goes in parentheses, 0.1(6). The calculator shows the bar form, a written-out version to 16 places, and a rounded value to 2, 3, 4 or 6 places for everyday use — the rounding is done on the exact digits, so 2/3 is 0.6667, not 0.6666.

Common fractions as decimals

Fraction	Decimal	Fraction	Decimal
1/2	0.5	1/3	0.3̅
1/4	0.25	2/3	0.6̅
3/4	0.75	1/6	0.16̅
1/5	0.2	5/6	0.83̅
1/8	0.125	1/7	0.1̅4̅2̅8̅5̅7̅
3/8	0.375	1/9	0.1̅
5/8	0.625	1/11	0.0̅9̅
7/8	0.875	1/12	0.083̅
1/16	0.0625	1/16 of an inch	1.5875 mm

Inch fractions on tape measures are all halves, quarters, eighths and sixteenths, so they always end; to add them as lengths, use the feet and inches calculator.

Decimals, percents and back

A percent is the decimal times 100: 3/8 = 37.5%, 1/6 = 16.6̅%. For percentages of amounts, increases and discounts, see the percentage calculator. To go from a decimal back to a fraction, or to add and simplify fractions before converting, the fraction calculator accepts decimals like 0.375 and returns 3/8. To put several fractions over one denominator first, find the least common denominator with the LCM calculator.

Frequently asked questions

How do you convert a fraction to a decimal?

Divide the top number by the bottom number. 3/8 is 3 ÷ 8 = 0.375. For a mixed number, convert the fraction part and add the whole number: 2 1/6 = 2 + 0.1666… = 2.1666…

What is 2/3 as a decimal?

0.666…, with the 6 repeating forever, written 0.6̅. Rounded, it is 0.67 to two places or 0.6667 to four.

Why do some fractions repeat and others end?

A fraction in lowest terms ends exactly when its denominator has no prime factors except 2 and 5, because those are the factors of 10. 3/8 and 7/20 end; 1/3, 1/6 and 5/7 repeat.

How do you write a repeating decimal?

Put a bar over the digits that repeat: 0.6̅ for 2/3, 0.1 6̅ for 1/6, and 0.7̅1̅4̅2̅8̅5̅ for 5/7. Some books use dots over the first and last repeating digits, and software often uses parentheses: 0.(714285).

How long can the repeating part be?

Up to one less than the denominator. 1/7 repeats every 6 digits, 1/17 every 16, and 1/97 every 96 digits.

How do I turn the decimal into a percent?

Multiply by 100, which moves the decimal point two places to the right: 3/8 = 0.375 = 37.5%, and 2/3 = 66.6̅%.