The short version
A decimal is a fraction that ran out of patience with the fraction bar. 0.75 is “seventy-five hundredths” — write that as a fraction and you get 75/100, then simplify to 3/4. That is the entire method: read it aloud, write the place value, simplify. The decimal to fraction converter does all three steps instantly, but the hand method below works anywhere — including on tests where calculators are banned.
Step 1: read it aloud
The place value of the last digit names the denominator. One digit after the point means tenths (0.4 = 4/10). Two digits means hundredths (0.75 = 75/100). Three means thousandths (0.125 = 125/1000). Four means ten-thousandths (0.0625 = 625/10000). Read the number the way you would say it — “seventy-five hundredths” — and the fraction practically dictates itself.
Step 2: simplify with the GCD
Raw place-value fractions are almost never in lowest terms, so find the greatest common divisor of the top and bottom and divide both by it. For 75/100, the GCD is 25: 75 ÷ 25 = 3, 100 ÷ 25 = 4 → 3/4. Quick GCD shortcuts: if both numbers end in 0 or 5, try 5; if both are even, keep halving; if one divides the other evenly, the smaller one is the GCD (125 goes into 1000 exactly eight times, so 125/1000 = 1/8 in one step). For anything stubborn, Euclid’s algorithm never fails — the fraction simplifier shows it working.
Worked example: 2.4
Whole numbers get their own treatment. 2.4 is “two and four tenths” — keep the 2 aside and convert 0.4: 4/10, simplify by the GCD of 2 → 2/5, giving 2 2/5 as a mixed number (or 12/5 as an improper fraction: 2 × 5 + 2 = 12, over 5). Same recipe for 3.125: 3 aside, 125/1000 = 1/8 → 3 1/8. The integer part never participates in the simplifying — it just waits at the front.
Repeating decimals: the algebra trick
Some decimals never end — 0.333…, 0.1666…, 0.142857142857… — and no place value can name them, because there is no last digit. Here algebra earns its keep. Take 0.333… and call it x. Multiply by 10: 10x = 3.333…. Subtract: 10x − x = 3.333… − 0.333… = 3. So 9x = 3 and x = 3/9 = 1/3. For 0.1666…: 10x = 1.666…, 100x = 16.666…, subtract → 90x = 15, x = 15/90 = 1/6. The repeating block cancels itself — that is the whole trick, and it works for any repeating pattern.
Common conversions worth memorizing
These show up everywhere — recipes, discounts, test questions, workshop math. Learn the row, skip the work:
| Decimal | Fraction | Percent |
|---|---|---|
| 0.5 | 1/2 | 50% |
| 0.25 | 1/4 | 25% |
| 0.75 | 3/4 | 75% |
| 0.2 | 1/5 | 20% |
| 0.4 | 2/5 | 40% |
| 0.6 | 3/5 | 60% |
| 0.8 | 4/5 | 80% |
| 0.125 | 1/8 | 12.5% |
| 0.375 | 3/8 | 37.5% |
| 0.625 | 5/8 | 62.5% |
| 0.875 | 7/8 | 87.5% |
| 0.1 | 1/10 | 10% |
Which form should you use?
Use decimals for calculating and comparing — calculators, spreadsheets, and prices all speak decimal, and 0.625 vs 0.6 settles instantly. Use fractions when exactness matters — 1/3 is precise where 0.333 is always a hair short. Use percents when a human needs the gut feeling: “75% off” lands where “0.75 off” confuses. The three forms are one number in three costumes — the converter, the chart, and the simplifier translate between all of them.
The bottom line: read the decimal aloud, write the place value as a fraction, simplify with the GCD. Repeating decimals get the algebra trick. Three steps, no calculator required.
Bright Side Kit. "How to Convert a Decimal to a Fraction." https://brightoolbox.com/guides/how-to-convert-decimal-to-fraction/ Accessed October 22, 2026.