Turn a fraction into its decimal and percentage form. The calculator also tells you if the decimal ends, or repeats forever.
The numerator is divided by the denominator.
Multiplying by 100 gives the percentage form.
A fraction terminates only if its reduced denominator has no prime factors other than 2 and 5 — otherwise the decimal repeats forever.
Decimal: Numerator ÷ Denominator
Percentage: Decimal × 100
Converting three eighths into a decimal.
Fraction: 3/8
Divide: 3 ÷ 8 = 0.375
As a percentage: 0.375 × 100 = 37.5%
The denominator 8 is 2³, so the decimal terminates
Answer: 0.375 (37.5%)
A fraction to decimal calculator divides the numerator by the denominator and gives the decimal and percentage form of the fraction. It also tells you whether the decimal ends after a few places or repeats forever, which is a question students are often asked to predict without doing the division.
Converting 5/12 or 7/8 into decimals makes comparison easy, because decimals line up digit by digit. It matters when entering marks out of a total into a spreadsheet, when comparing fractional discounts, and in Class 9 and 10 where students learn the rule that decides terminating and non-terminating recurring decimals. The calculator shows the reduced fraction too, since the rule works only on the fraction in lowest terms.
1. Reduce the fraction to lowest terms by dividing top and bottom by their HCF.
2. Factorise the reduced denominator into primes.
3. If the only prime factors are 2 and 5, the decimal terminates; otherwise it repeats.
4. Divide the numerator by the denominator by long division to get the decimal.
5. For a repeating decimal, continue until a remainder repeats; the digits between the repeats form the cycle.
6. Multiply the decimal by 100 to get the percentage.
A decimal terminates if it can be written as a whole number over a power of ten. Since 10ⁿ = 2ⁿ × 5ⁿ, a fraction in lowest terms can be scaled to a power-of-ten denominator only if its denominator has no prime factors other than 2 and 5. So 3/8 = 375/1000 terminates, while 5/12 cannot, because 12 = 2² × 3 and no power of ten is divisible by 3. The rule must be applied after reducing: 6/15 looks bad, but it reduces to 2/5 = 0.4.
In long division by d, each remainder is one of 0, 1, 2, ..., d − 1. If a remainder of 0 never appears, there are only d − 1 possible remainders, so within d − 1 steps one must recur. From that point the division repeats exactly, producing a cycle of digits. This proves every fraction gives either a terminating or a repeating decimal, and it bounds the cycle length: 1/7 repeats every 6 digits, the maximum possible for 7.
The decimal shown is rounded, because a screen cannot show infinitely many digits. For 5/12 = 0.41666..., the 6 repeats forever, and the correct notation is 0.41 followed by 6 with a bar over it. When you use a rounded decimal in further work, errors accumulate. In exams, keep answers as fractions until the last step, and round only as the question instructs. The percentage form is the decimal multiplied by 100 and carries the same rounding.
Tanvi answered 5 out of every 12 questions correctly in a practice set and wants the fraction as a decimal and percentage.
Answer: Decimal 0.4166666667; As a percentage 41.666667%; Simplified fraction 5/12
Applying the 2s and 5s rule before reducing the fraction, such as calling 3/6 non-terminating.
Dividing the denominator by the numerator, which gives the reciprocal.
Writing a repeating decimal like 0.41666... as 0.416 and treating it as exact.
Forgetting that a negative fraction gives a negative decimal and percentage.
Predicting terminating or repeating decimals in Class 10 real numbers questions.
Converting scores out of a total into percentages for report cards.
Comparing fractional offers such as 'one-third off' against a percentage discount.
Entering fractional quantities into spreadsheets or billing software that expects decimals.
Why do some fractions give repeating decimals?
Our number system uses base 10, which breaks down into 2 and 5. A fraction only ends if its simplified bottom number is made only of 2s and 5s. A bottom number like 3, 7, or 11 does not divide evenly into 10, so the division never ends.
How do I write a repeating decimal?
With a bar or dot over the repeating part — 1/3 is written as 0.3 with a bar over the 3. This calculator shows the rounded decimal, and tells you that it repeats.