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.
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.
Practice Questions
- Write 7/8 as a decimal.
- Write 5/6 as a decimal (recurring).
- Convert 2 and 3/4 to a decimal.
- Which is greater: 3/7 or 0.43?
- A tile is 3/8 m wide. Express this in decimal metres.