Fraction to Decimal Converter

Convert any fraction to its decimal equivalent with repeating decimal detection.

Fraction to Decimal Converter tool

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Example

Input: Numerator 3, denominator 8 (3/8)

Result: 0.375 (37.5 %, terminating decimal)

3 / 8 = 0.375. It terminates because the denominator 8 = 2^3 has no prime factors other than 2 and 5.

Common Fractions as Decimals

FractionDecimalRepeating formPercent
1/20.5Terminates50%
1/30.33333333330.(3)33.333333%
2/30.66666666670.(6)66.666667%
1/40.25Terminates25%
3/40.75Terminates75%
1/50.2Terminates20%
1/60.16666666670.1(6)16.666667%
1/70.14285714290.(142857)14.285714%
1/80.125Terminates12.5%
3/80.375Terminates37.5%
1/90.11111111110.(1)11.111111%
1/110.09090909090.(09)9.090909%
1/120.08333333330.08(3)8.333333%
1/160.0625Terminates6.25%

Digits in brackets repeat forever. Decimals rounded to 10 places, as the converter shows them.

  1. Enter the numerator and denominator of the fraction you want to convert.
  2. View the decimal equivalent calculated instantly.
  3. Check whether the result is a terminating or repeating decimal.
  4. For repeating decimals, see the repeating digits shown in parentheses, plus the non-repeating part if there is one.
  5. Click the copy button to copy the decimal result.

When Does a Fraction Give a Repeating Decimal?

To turn a fraction into a decimal, divide the top number by the bottom number: 3/8 is 3 divided by 8, which is 0.375. This converter does the division, gives the percent, and tells you whether the decimal ends or repeats forever. For repeating decimals it puts the repeating block in brackets, so 1/7 shows as 0.(142857).

Whether a decimal ends depends only on the bottom number. Put the fraction in lowest terms first. If the denominator has no prime factors other than 2 and 5, the decimal stops. So 3/8 ends, because 8 is 2 x 2 x 2. But 1/6 repeats, because 6 has a factor of 3. Every fraction of whole numbers either ends or repeats. It never runs on at random.

The bracket form is exact, while the plain decimal is rounded. For 2/3 the Decimal result shows 0.6666666667, rounded to 10 places. The repeating form 0.(6) is the true value. Some fractions start with digits that do not repeat. For 1/6 the tool shows 0.1(6): the 1 appears once and then the 6 repeats. It lists the non-repeating part and the repeating digits on their own lines too.

Some repeating blocks are long. The block for 1/7 is 6 digits, and for 1/97 it is 96 digits. The converter finds blocks up to 5,000 digits long. Repeat detection works for whole-number inputs only. To go the other way, use the Decimal to Fraction Converter. To express a fraction as a share of a total, the Percentage Calculator has more options.

Formula / How It Works

Decimal = Numerator / Denominator

Frequently Asked Questions

Divide the numerator by the denominator. For 3/4 that is 3 divided by 4, which is 0.75. By hand, use long division and keep adding zeros after the decimal point until the digits stop or start to repeat. Multiply the decimal by 100 to get the percent, so 0.75 is 75%.
The digits inside the brackets repeat forever. So 0.(3) means 0.3333 and so on, which is exactly 1/3. Textbooks often draw a bar over the repeating digits or put dots above them instead. All three styles mean the same thing. The bracket style is used here because it is easy to type and copy.
A fraction in lowest terms gives a decimal that ends only if its denominator has no prime factors other than 2 and 5. For example, 7/40 ends, because 40 = 2 x 2 x 2 x 5, and it equals 0.175. But 1/12 repeats, because 12 has a factor of 3. It shows as 0.08(3).
The plain Decimal result is rounded to 10 decimal places, so the last 6 rounds up to 7. The exact value is in the Repeating Decimal result, 0.(6). Use the rounded value for everyday math, and the repeating form when you need to show the exact answer.

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