Converting a fraction to a decimal is division: the fraction a/b means "a divided by b," so 3/4 as a decimal is 3 ÷ 4 = 0.75. Some fractions convert to a decimal that terminates cleanly (3/4 = 0.75, 1/8 = 0.125), while others repeat forever (1/3 = 0.333..., 1/7 = 0.142857142857...). Whether a fraction terminates depends entirely on its denominator once fully simplified: if the simplified denominator's only prime factors are 2 and/or 5 (the prime factors of 10, our base), the decimal terminates; if any other prime factor is present, it repeats. That's why 1/4 (denominator 2²) terminates but 1/3 (denominator 3) repeats, and why 7/20 (denominator 2² × 5) terminates but 5/6 (denominator 2 × 3) repeats.
Worked example one: 5/8 as a decimal. 5 ÷ 8 = 0.625, and it terminates because 8 = 2³, all factors of 2. Worked example two: 2/9 as a decimal. 2 ÷ 9 = 0.2222..., repeating, because 9 = 3², and 3 isn't a factor of 10.
Converting the Other Direction
Converting the other direction — decimal to fraction — depends on whether the decimal terminates or repeats. For a terminating decimal, write it over the appropriate power of 10 based on how many digits follow the decimal point, then simplify: 0.375 has three decimal places, so it's 375/1000, which simplifies (dividing both by their GCF, 125) to 3/8. For a repeating decimal, the method is algebraic: let x = 0.777..., then 10x = 7.777..., and subtracting the first equation from the second gives 9x = 7, so x = 7/9.
Common Mistakes Converting
A common mistake with terminating decimals is misreading the place value — writing 0.75 as 75/1000 instead of 75/100 (0.75 has two decimal places, not three), which changes the answer entirely before you even get to simplifying. A second common mistake is stopping before fully simplifying: 375/1000 is technically correct but not in lowest terms, and most contexts (and the Simplify Fractions Calculator) expect the reduced form, 3/8.
Common Pairs Worth Memorizing
Recognizing a handful of common fraction-decimal pairs by memory speeds up everyday estimation considerably: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/8 = 0.125, and 1/3 ≈ 0.333. Mixed numbers (like 2 3/4) convert the same way as proper fractions, just adding the whole-number part back on after converting the fractional part: 2 3/4 = 2 + 0.75 = 2.75. Improper fractions (where the numerator is larger than the denominator, like 11/4) convert identically through straight division — 11 ÷ 4 = 2.75 — arriving at the same result without needing to separate out a whole-number part first.
Percentage is a natural third form alongside fraction and decimal — a decimal converts to a percentage by multiplying by 100 (0.75 → 75%), and a fraction converts to a percentage the same way after first becoming a decimal. A related but distinct repeating pattern worth recognizing: some fractions repeat with more than one digit in the repeating block. 1/7 = 0.142857142857..., where the six-digit block "142857" repeats indefinitely — and, notably, that repeating block is itself the cyclic number discussed on this site's notable-numbers pages, since multiplying it by 2 through 6 just cycles its digits. Not every repeating decimal has such a striking pattern, but the underlying reason all sevenths repeat with a six-digit block traces back to the same denominator-factorization rule covered above.
If your next step after converting is simplifying the fraction itself, use the Simplify Fractions Calculator; for the full method with more worked examples in both directions, see How to Convert a Fraction to a Decimal and its companion, How to Convert a Decimal to a Fraction.