Fraction to Decimal Calculator

How to use the fraction to decimal calculator

1. Enter the fraction. For a plain fraction such as 43/22, leave the whole number at 0. For a mixed number such as 2 3/8, enter 2, 3 and 8.
2. Switch on Negative for a negative value. The sign applies to the whole mixed number.
3. Read the exact decimal. A repeating block is shown in parentheses: 1.9(54) means 1.954545… with the 54 going on forever. The panel also shows the value rounded to six places, the percent, the fraction in lowest terms and the prime factors of its denominator.

The division is done with whole numbers digit by digit, the same way you would on paper, so the repeating block is exact even when it is hundreds of digits long.

The method: a fraction bar means divide

The open textbook Prealgebra 2e from OpenStax puts it simply: a fraction bar means division. 3/4 is 3 ÷ 4 = 0.75 (Example 5.28), and −7/2 is −(7 ÷ 2) = −3.5 (Example 5.29).

When the division doesn’t come out even, keep bringing down zeros and watch the remainders. Example 5.30 divides 43 by 22:

The moment a remainder repeats, every digit after it repeats too, because the division from that point is identical. There are only as many possible remainders as the denominator, so a repeat must show up within that many steps. The calculator records each remainder and where it first appeared, which is how it finds the start and length of the block.

Will the decimal stop or repeat?

You can tell before dividing. Reduce the fraction to lowest terms and factor the denominator:

• Only 2s and 5s: the decimal terminates. 7/40 = 0.175 because 40 = 2³ × 5. 3/8 = 0.375, 1/20 = 0.05.
• Any other prime: the decimal repeats. 1/3 = 0.(3), 5/12 = 0.41(6), 1/7 = 0.(142857), 1/11 = 0.(09).

The reason: a decimal that stops is a whole number over a power of ten, and the only prime factors of 10, 100 or 1000 are 2 and 5. A denominator with a 3 or a 7 in it can’t divide any power of ten.

Reduce first. 3/6 looks like it has a 3 in the denominator, but it is 1/2, which is 0.5.

The repeating block can be long. For a denominator that shares no factor with 10, the block has fewer digits than the denominator itself. 1/7 repeats every 6 digits, 1/13 every 6, and 1/17 every 16. When the denominator has 2s or 5s and other primes, as 12 does, a few digits come first before the cycle begins: 5/12 = 0.41666….

Common fractions as decimals

• Halves and quarters: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75.
• Eighths: 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875.
• Sixteenths: 1/16 = 0.0625, 3/16 = 0.1875, 5/16 = 0.3125.
• Thirds and sixths: 1/3 = 0.(3), 2/3 = 0.(6), 1/6 = 0.1(6), 5/6 = 0.8(3).
• Fifths and tenths: 1/5 = 0.2, 2/5 = 0.4, 1/10 = 0.1.
• Ninths: 1/9 = 0.(1), 2/9 = 0.(2), and so on up to 8/9 = 0.(8).

Eighths and sixteenths are worth remembering for measurements, since rulers, wrenches and drill bits use them. Ninths have the neat pattern that the numerator becomes the repeating digit.

Rounding and percents

For most practical uses you round. Look at the digit after the place you want to keep: 5 or more rounds up. 2/3 to two places is 0.67; 1/6 to three places is 0.167. Rounding a repeating decimal loses a little accuracy, so if you plan to keep calculating, carry the fraction and round only at the end.

To get a percent, multiply the decimal by 100. 3/8 = 0.375 = 37.5%; 2/3 = 66.67% to two places. A grade of 17 out of 20 is 17/20 = 0.85 = 85%.

To go the other way, from a decimal such as 0.8(3) back to 5/6, use the decimal to fraction calculator; it accepts the same parentheses notation.

Mixed numbers and improper fractions

For a mixed number, only the fraction part needs dividing: 2 3/8 = 2 + 0.375 = 2.375. Converting to an improper fraction first gives the same answer: 19/8 = 19 ÷ 8 = 2.375.

An improper fraction such as 43/22 gives a decimal greater than 1, and the whole-number part comes from the first step of the long division.

With a negative mixed number, the sign covers the whole value: −1 1/4 = −1.25, not −1 + 0.25.

Worked conversions to practice on

• 5/16: 16 = 2⁴, so it terminates. 5 ÷ 16 = 0.3125.
• 11/40: 40 = 2³ × 5, so it terminates. 11 ÷ 40 = 0.275.
• 7/12: 12 = 2² × 3, so it repeats after two fixed digits. 7 ÷ 12 = 0.58333… = 0.58(3).
• 3/11: the remainders cycle 3, 8, 3, so two digits repeat. 3 ÷ 11 = 0.(27).
• 2/7: six digits repeat, the same six as 1/7 starting at a different point. 2 ÷ 7 = 0.(285714).
• 1/13: six repeating digits again. 1 ÷ 13 = 0.(076923).

Enter any of these to compare your long division with the calculator’s, including the repeating block.

Very long repeating blocks

Some denominators produce surprisingly long cycles. 1/17 repeats every 16 digits, and 1/97 every 96 digits, the most it could, since there are only 96 nonzero remainders when dividing by 97. A handheld calculator with ten or twelve digits on screen can’t show you where such a cycle starts again, so it displays a rounded value that looks like it doesn’t repeat at all.

The calculator here keeps dividing until a remainder repeats, for up to 2,000 digits, and prints the full block. For everyday use, the six-place rounded figure beside it is usually all you need.

Fractions in a spreadsheet

Typing 3/8 into a spreadsheet cell can turn it into a date, such as March 8. Enter it as a formula, =3/8, and the cell holds 0.375. In Excel you can also type a zero and a space first, as in 0 3/8, to enter it as a number; a mixed number works the same way, as 2 3/8. Formatting the cell as a fraction changes only the display, so the stored value is still the rounded decimal, and long repeating blocks are cut off at about fifteen digits.

Sources & assumptions

How this calculator gets its numbers. Full method: our methodology.

• The decimal comes from whole-number long division, digit by digit.
• A repeating block starts where a remainder first repeats; it is shown in parentheses.
• A reduced fraction terminates only if its denominator has no prime factors other than 2 and 5.
• Long division stops after 2,000 digits; denominators up to one billion are accepted.

Sources

1. OpenStax (Rice University), Prealgebra 2e, 5.3 Decimals and Fractions. A fraction bar means division (3/4 = 0.75, −7/2 = −3.5) and repeating decimals by long division, including Example 5.30, 43/22 = 1.9 with 54 repeating.

Last reviewed November 2, 2026. For further calculation, carry the fraction and round the decimal only at the end.