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. A terminating decimal goes over the matching power of 10 (however many digits sit after the point) and then gets reduced: 0.44 has two decimal places, so it starts as 44/100, and dividing both by their GCF of 4 lands on 11/25. A repeating decimal needs an algebraic trick instead — let x = 0.222..., multiply by 10 to shift one full repeat (10x = 2.222...), and subtract the original equation to cancel the repeating tail: 9x = 2, so x = 2/9.
Common Mistakes Converting
A common mistake with terminating decimals is misreading the place value — treating 0.6 as if it had two decimal places instead of one, writing 6/100 rather than the correct 6/10 (which reduces to 3/5). A second common mistake is stopping before fully simplifying: 44/100 is technically a valid fraction but not in lowest terms, and most contexts (and the Simplify Fractions Calculator) expect the reduced form.
Common Pairs Worth Memorizing
A handful of fraction-decimal pairs are worth having on instant recall rather than re-deriving each time: a half is 0.5, a quarter is 0.25, three-quarters is 0.75, a fifth is 0.2, and an eighth is 0.125. Mixed numbers convert by handling the whole-number part separately and just converting the fractional remainder — 3 1/4 becomes 3 + 0.25 = 3.25. Improper fractions, where the numerator outsizes the denominator, convert through the same straight division without any extra step: 13/4 as a decimal is simply 13 ÷ 4 = 3.25.
Percentage rounds out the trio — a decimal becomes a percentage by multiplying by 100 (0.6 → 60%), and a fraction gets there by converting to a decimal first and then applying that same step. Worth a special mention: sevenths repeat in a distinctive six-digit block (1/7 = 0.142857142857...) where "142857" is itself a well-known cyclic number, since multiplying it by 2 through 6 just rotates its own digits rather than producing something unrelated — a genuinely striking pattern most repeating fractions don't share.
One more distinction worth having straight: not every repeating decimal starts repeating from the very first digit. 1/6 = 0.1666..., where the 1 appears once and only the 6 repeats forever after it — a "mixed" repeating decimal, as opposed to 1/3's pure repeat from the first digit onward. Whether a fraction produces a pure or mixed repeat depends on whether its denominator, once simplified, has any factors of 2 or 5 mixed in alongside the non-2-non-5 prime that forces the repetition in the first place; 6 = 2 × 3 carries exactly that mix, which is why 1/6 gets a short non-repeating lead-in before settling into its repeating tail.
If your next step after converting is simplifying the fraction itself, use the Simplify Fractions Calculator; the dedicated guides for each direction go deeper on the reasoning and cover several more worked cases.