How to Convert a Fraction to a Decimal (Step-by-Step)

The short version

A fraction like 3/4 means 3 divided by 4 — that is all the bar ever meant. So 3 ÷ 4 = 0.75, and you are done. Type any fraction into the fraction to decimal converter and it does the division for you, including spotting digits that repeat forever. The rest of this guide is for the times you need to do it by hand — or want to understand what the digits are doing.

Long division, step by step: 3/4

Set it up as 4 going into 3.000. The decimal point goes directly above, and the zeros are free — you can add as many as the division needs.

Step 1: 4 does not go into 3, so write 0. and look at 30. Step 2: 4 goes into 30 seven times (7 × 4 = 28). Write 7 after the point; the remainder is 2. Step 3: bring down the next 0, making 20. 4 goes into 20 exactly five times, remainder 0. Answer: 0.75.

The pattern is always the same: divide, multiply back, subtract, bring down a zero, repeat until the remainder is 0. Try 7/8 the same way: 8 into 7.000 gives 0 (point), 8 into 70 goes 8 times (64, remainder 6), 8 into 60 goes 7 times (56, remainder 4), 8 into 40 goes 5 times exactly. 7/8 = 0.875.

Why some decimals never end: the 2s-and-5s rule

Now try 1/3. 3 goes into 1.0 zero times, into 10 three times (9), and the remainder is 1 again. Bring down another zero and you get the same remainder, the same 3, forever: 0.333…. It never terminates — and you can know that before dividing.

Simplify the fraction, then factor the denominator. If its only prime factors are 2s and 5s — like 4 (2²), 8 (2³), 20 (2²×5), or 32 (2⁵) — the decimal terminates, because 10 itself is just 2×5. Any other prime factor (3, 7, 11, …) means the division can never come out even, so the digits repeat. Here is the rule of thumb: denominators built from 2s and 5s stop; everything else loops.

Reading repeating decimals

A repeating digit gets a bar over it in textbooks, or parentheses in plain text: 1/6 = 0.1666… is written 0.1̄6̄ or 0.1(6) — the 6 repeats forever. Some fractions repeat in blocks: 1/7 = 0.(142857), the same six digits cycling endlessly. Writing “0.333…” is fine for conversation, but the bar or parentheses version is the precise one — it says exactly which digits repeat and promises there are infinitely many of them.

From fractions to decimals to percents

A percent is just a decimal multiplied by 100, so the chain is: fraction → decimal → percent. 3/4 → 0.75 → 75%. 1/8 → 0.125 → 12.5%. 2/3 → 0.666… → 66.67% (rounded). Memorize the big ones and you will rarely reach for a calculator: halves (0.5), quarters (0.25, 0.75), eighths (0.125, 0.375, 0.625, 0.875), fifths (0.2, 0.4, 0.6, 0.8), and tenths (0.1, 0.3, 0.7, 0.9). The full set lives on the fraction to decimal chart, including every 32nd the way tape measures go.

Going backward: decimal to fraction

Read the decimal aloud and the fraction writes itself: 0.75 is “seventy-five hundredths” → 75/100, which simplifies to 3/4 (divide top and bottom by 25). 0.125 is “one hundred twenty-five thousandths” → 125/1000 = 1/8. Repeating decimals need a small trick: for 0.333…, call it x. Then 10x = 3.333…, and 10x − x = 3, so 9x = 3 and x = 3/9 = 1/3. The same algebra works for any repeating block.

Which form should you use?

Use decimals when you are calculating or comparing — a calculator and a spreadsheet speak decimal, and 0.625 vs 0.6 settles a comparison instantly. Use fractions when exactness matters — 1/3 is precise while 0.333 is always a hair short, which is why carpenters cut to fractions and engineers calculate to decimals. And use percents when a human needs the gut feeling: “75% off” lands in a way “3/4 off” never will.

The bottom line: the fraction bar is a division sign — divide the top by the bottom. Denominators made only of 2s and 5s terminate; everything else repeats. Decimals calculate, fractions stay exact, percents persuade. Skip the hand work anytime on the fraction to decimal chart and converter.