The formula this page uses
a/b = a ÷ b. It terminates only when b, in lowest terms, has no prime factors except 2 and 5.
Convert fractions to decimals, with steps
Use the free fraction to decimal calculator to work through the number relationship, preserve exact values, and check the result with estimation. Choose a focused operation below to calculate, inspect the method, and connect the result to a visual model.
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Arithmetic
Fraction to Decimal Calculator explained
The short version
- The line in a fraction is a division sign, so 5/8 just means 5 divided by 8.
- The top number goes inside the division, not the bottom one.
- The decimal stops only if the bottom number is built from 2s and 5s; anything else repeats forever.
What each part means
SymbolWhat it means
a — NumeratorThe top number. It is the one being divided, so it goes inside the division box.
b — DenominatorThe bottom number. It does the dividing and it decides whether the decimal ends.
remainder — What is left at each stepA remainder of 0 means the decimal stops. A repeated remainder means it repeats.
the bar — Repeating notationA line drawn over the digits that repeat, as in 0.416 with a bar over the 6.
Show your work: a full example
- Convert 5/85 ÷ 8
- 8 does not go into 5, so write 0. and add a zero50 ÷ 8 = 6 remainder 2, so far 0.6
- Bring down another zero20 ÷ 8 = 2 remainder 4, so far 0.62
- And another40 ÷ 8 = 5 remainder 0, so far 0.625
- Remainder 0 means the division has finished5/8 = 0.625
- Check the bottom number8 = 2 × 2 × 2, only 2s, which is why it stopped
A second, different case
- A different case: the decimal never ends5/12
- First step50 ÷ 12 = 4 remainder 2, so far 0.4
- Second step20 ÷ 12 = 1 remainder 8, so far 0.41
- Third step80 ÷ 12 = 6 remainder 8, so far 0.416
- The remainder 8 has come backthe same step will repeat forever, so the 6 repeats
- Write it properly5/12 = 0.41666…, or 0.416 with a bar over the 6
- Check the bottom number12 = 2 × 2 × 3, and the 3 is what stops it ending
Copy-ready example
5 ÷ 8
Convert 5/8
Questions about the Fraction to Decimal Calculator
Can I tell whether a fraction repeats before doing the division?
Yes. Reduce it first, then factor the bottom number. 7/40 has 40 = 2 × 2 × 2 × 5, so it terminates at 0.175. 7/30 has 30 = 2 × 3 × 5, and that 3 guarantees a repeat. This check takes five seconds and saves a long division that was never going to end.
How long can a repeating block get?
At most one less than the bottom number, because there are only that many possible remainders before one has to come back. For sevenths the block is six digits long, which is the maximum. For elevenths it is only two, even though ten were allowed.
What does the bar over the digits mean?
It marks exactly which digits repeat. In 0.416 with the bar over only the 6, the 4 and 1 happen once and the 6 goes on forever. If the bar covered 416 it would mean 0.416416416…, which is a completely different number.
How do I convert a mixed number like 2 and 3/8?
Convert just the fraction part and add the whole number back on. 3 ÷ 8 = 0.375, so 2 and 3/8 = 2.375. You get the same answer from the improper fraction 19/8, since 19 ÷ 8 = 2.375.
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