A fraction is really an unfinished division problem — the bar between numerator and denominator is a division sign that fraction notation lets you leave unsolved. 5/8 doesn't just *represent* 5 ÷ 8; it *is* 5 ÷ 8, just written in a paused state. Carrying out the division that the fraction bar is quietly asking for is all "converting to a decimal" means.
Working Through the Long Division
5 ÷ 8 by hand: 8 doesn't go into 5, so the answer starts at 0, and the division continues into decimal places by attaching zeros to the remainder. 50 ÷ 8 = 6 remainder 2 (0.6), 20 ÷ 8 = 2 remainder 4 (0.62), 40 ÷ 8 = 5 remainder 0 (0.625) — the remainder hits zero, so the division is finished exactly. 5/8 = 0.625.
Why Some Fractions Terminate and Others Repeat Forever
Our number system is built on powers of 10, and 10's only prime building blocks are 2 and 5. A fraction's long division can only ever land on a remainder of exactly zero — finishing cleanly — if the denominator (once fully reduced) is made of nothing but those same two primes, because only then can the fraction be rewritten as some whole number over a power of 10. The moment a denominator carries a prime factor outside {2, 5} — a 3, a 7, an 11 — there's no power of 10 it evenly divides into, so the long division can never land on a zero remainder and is mathematically guaranteed to cycle through remainders forever instead. 5/8 terminates because 8 = 2³. 1/3 repeats (0.333...) because 3 shares nothing with 10. 7/20 terminates because 20 = 2² × 5. 5/6 repeats because the 3 hiding inside 6 = 2 × 3 has no home in a power of 10.
A quick estimate-first habit worth building before any division: is the fraction closer to 0, 0.5, or 1? 2/9 is well under 1/2, so its decimal should be a small value under 0.5 — and 0.222... is. This rough positioning check, done in seconds without any division, catches a badly wrong answer (like accidentally computing 9÷2 instead of 2÷9) immediately.
Worked example: 2/9 as a decimal. 2 ÷ 9: 20 ÷ 9 = 2 remainder 2 (0.2), 20 ÷ 9 = 2 remainder 2 again (0.22) — the remainder has repeated, meaning the digit sequence will repeat forever. 2/9 = 0.222... This is written with a bar over the repeating digit(s) in formal notation: 0.2̄.
Worked example: 1/7 as a decimal. 1 ÷ 7 works out to 0.142857142857..., with the six-digit block "142857" repeating indefinitely. This particular repeating block is famous in its own right — it's a cyclic number, meaning multiplying it by 2 through 6 just cycles its own digits around (142857 × 2 = 285714, which is the same six digits starting from a different point in the cycle).
Recognizing common fraction-decimal pairs. A handful of conversions are worth memorizing for speed, since they come up constantly: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 2/5 = 0.4, 1/8 = 0.125, 1/10 = 0.1, and 1/3 ≈ 0.333. Recognizing these on sight, rather than dividing them out every time, speeds up mental estimation considerably.
Mixed numbers. A mixed number like 3 1/4 converts by leaving the whole-number part as is and converting only the fractional part, then adding them back together: 1/4 = 0.25, so 3 1/4 = 3.25.
Common Mistakes Converting to Decimal
The most frequent error is stopping the division too early on a fraction that terminates further out than expected — treating 0.62 as the final answer for 5/8 instead of continuing one more step to the exact 0.625. A second common mistake happens with repeating decimals specifically: rounding a repeating decimal (writing 1/3 as exactly 0.33) and then treating that rounded value as exact in further calculations, which introduces a small but compounding error — 0.33 × 3 = 0.99, not the true 1 that 1/3 × 3 equals exactly.
Converting the other direction. Going from decimal back to fraction uses a different method depending on whether the decimal terminates or repeats — covered in the companion guide, How to Convert a Decimal to a Fraction, which also explains the algebraic trick for handling repeating decimals specifically.
Worked example: convert 11/16 to a decimal. 11 ÷ 16: 110÷16=6 remainder 14 (0.6), 140÷16=8 remainder 12 (0.68), 120÷16=7 remainder 8 (0.687), 80÷16=5 remainder 0 (0.6875), done. 11/16 = 0.6875, terminating, since 16=2⁴, all factors of 2.
Worked example: convert 4/11 to a decimal, another repeating case. 4÷11: 40÷11=3 remainder 7 (0.3), 70÷11=6 remainder 4 (0.36), 40÷11=3 remainder 7 again (0.363) — the remainder 7 has reappeared, so the pattern "36" repeats from here. 4/11 = 0.363636..., a two-digit repeating block, because 11 is a prime factor with no relationship to 10.
A quick way to predict how many digits a repeating decimal's block will have, without doing the full division first. For a fraction with a prime denominator p (other than 2 or 5), the repeating block's length is always a divisor of p−1. For 1/7 (p=7), the block length divides 6, and turns out to be the full 6 digits (142857). For 1/11 (p=11), the block length divides 10, and turns out to be 2 digits (09, giving 0.090909...). This won't tell you the digits themselves, but it's a useful check on whether you've found the complete repeating pattern or stopped partway through it.
Estimating a decimal's rough value before doing the full division, as a sanity check. For 5/8, since 5 is a little more than half of 8, the decimal should land a bit above 0.5 — and 0.625 does. This kind of rough estimate, checked in seconds, catches a fully wrong answer (like accidentally computing 8÷5 instead of 5÷8) before it goes any further into a larger calculation.
Worked example: convert a fraction whose denominator is a larger prime, 3/13, showing a longer repeating block. 3 ÷ 13 works out to 0.230769230769..., with a six-digit repeating block ("230769"). Longer repeating blocks like this are common with prime denominators that share no factors with 10, and there's no shortcut around actually carrying out the long division to find the specific digits, even though the block-length rule mentioned above can predict how long the pattern will run.
Worked example: convert a fraction with a denominator that mixes prime factors 2 and 5, guaranteeing termination but requiring a few decimal places, 7/40. 40=2³×5. 7÷40: 70÷40=1 remainder 30 (0.1), 300÷40=7 remainder 20 (0.17), 200÷40=5 remainder 0 (0.175), done. 7/40=0.175, terminating after three decimal places, consistent with the denominator's prime factorization containing only 2's and 5's.
Once you have a fraction's decimal form, converting to a percentage is just one more step — multiply by 100, so 0.625 becomes 62.5%, exactly as covered in How to Calculate a Percentage.