Fraction to Decimal: the Division Trick (+ Converter & Chart)

Every fraction is secretly a division problem wearing a costume. 3/4 means “3 divided by 4” — do the division, get 0.75, done. This page has the instant converter, the chart worth taping to the fridge, and the honest answer to “why does 1/3 go on forever?”

The one rule: top divided by bottom

A fraction bar and a division sign are the same symbol drawn differently. 3/8 = 3 ÷ 8. Punch it into long division (or a calculator, we don’t judge) and out comes 0.375. That’s the entire method — everything else on this page is just practice and pattern-spotting.

By hand, it’s the same long division your child already knows, with one twist: since 3 is smaller than 8, you write 3 as 3.000 and keep dividing past the decimal point. 8 into 30 goes 3 times (24), remainder 6; 8 into 60 goes 7 times (56), remainder 4; 8 into 40 goes exactly 5. Answer: 0.375.

Common conversions chart

These are the ones worth just knowing — they show up in cooking, woodworking, money, and every math class from grade 4 up:

Why some decimals repeat forever

Try 1/3 by long division: 3 into 10 goes 3, remainder 1. Bring down a zero — 3 into 10 goes 3, remainder 1. You’re trapped in a loop, and the answer is 0.3333… repeating to infinity. Here’s the pattern worth teaching: if the denominator’s only prime factors are 2s and 5s, the decimal ends cleanly (halves, quarters, fifths, eighths, tenths, sixteenths). Any other prime in the bottom — 3, 7, 11 — and the decimal repeats forever. That’s why 7/8 terminates but 1/7 spins out 0.142857-142857… like a merry-go-round.

Going the other direction

Turning 0.375 back into 3/8 is its own two-step trick — we cover it (with its own converter) in our decimal to fraction guide. The two skills together are what “fraction-decimal fluency” actually means, and they lean on equivalent fractions and simplifying underneath.

When the division keeps going wrong

If your child can recite “top divided by bottom” but the long division itself falls apart, that’s not a fractions problem — it’s a division-fluency gap wearing a fractions costume, and more worksheets on fractions won’t fix it. (Our free printable packs include division-facts sheets if you want targeted reps.) It’s also exactly the kind of gap MathKnights’ adaptive quests are built to find: the game notices which step breaks and drops the difficulty to rebuild it, with a robot who thinks wrong answers are just plot twists. Free plan, no card, grades 1–5. ⚔️