Converting Fractions to Decimals
Every fraction can be written as a decimal. Knowing how to convert between the two forms helps you compare values, use a calculator, and understand measurements.
Decimal notation itself is a relatively recent invention compared to fractions — the Flemish mathematician Simon Stevin popularised decimal fractions in Europe with his 1585 pamphlet De Thiende (“The Tenth”), arguing that all merchants, surveyors, and astronomers should adopt base-10 fractions for the sake of easier calculation. Before that, most cultures (including the Babylonians with base 60, and European tradespeople with fractions like halves and quarters) worked entirely in ordinary fractions. Today the conversion runs constantly in the background of daily life: a calculator turning 3/4 into 0.75, a spreadsheet displaying “=A1/B1”, or a GPS reporting a distance of 2.5 km instead of 2½ km.
Why Convert?
Calculators, spreadsheets, and most measurement tools use decimals. Converting a fraction to a decimal lets you use these tools easily.
Method 1 – Long Division
Divide the numerator by the denominator. The result is the decimal. This always works for any fraction.
3 divided by 4: 4 goes into 3 zero times. Write 0. and add a zero: 30 divided by 4 = 7 remainder 2. 20 divided by 4 = 5. Answer: 0.75.
5.000 divided by 8. 50/8=6 r2; 20/8=2 r4; 40/8=5. Answer: 0.625.
Method 2 – Equivalent Fraction with Denominator 10, 100, or 1000
If the denominator only has factors of 2 and 5, you can multiply it to reach a power of 10.
Multiply top and bottom by 2: 6/10 = 0.6.
25 times 4 = 100. Multiply top and bottom by 4: 28/100 = 0.28.
Terminating vs Recurring Decimals
| Fraction | Decimal | Type |
|---|---|---|
| 1/2 | 0.5 | Terminating |
| 1/4 | 0.25 | Terminating |
| 1/8 | 0.125 | Terminating |
| 1/3 | 0.333... | Recurring |
| 2/3 | 0.666... | Recurring |
| 1/7 | 0.142857... | Recurring |
A fraction gives a terminating decimal only when its denominator (in lowest terms) has no prime factors other than 2 and 5.
Common Fractions to Remember
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/5 | 0.2 |
| 1/8 | 0.125 |
| 1/10 | 0.1 |
| 1/3 | 0.333... |
| 2/3 | 0.666... |
Mixed Numbers to Decimals
Whole number stays: 3. Convert 2/5 = 0.4. Answer: 3.4.
Key Takeaways
- Divide numerator by denominator to get the decimal form of any fraction.
- Fractions with denominators made only of 2s and 5s produce terminating decimals.
- Other fractions produce recurring decimals.
- Memorise the common fractions to speed up your work.