Converting Decimals to Fractions
Every decimal can be written as a fraction. Converting between the two forms gives you flexibility when calculating and helps you see connections between numbers.
Why Convert?
Some calculations are easier with fractions (e.g., dividing by 1/2 is the same as multiplying by 2). Converting a decimal to a fraction is also necessary for exact answers, because fractions like 1/3 cannot be written as a terminating decimal.
Method – Using the Place Value of the Last Digit
1. Write the decimal as a fraction with a power of 10 as the denominator.
2. The denominator is 10 if there is one decimal place, 100 for two, 1000 for three, etc.
3. Simplify the fraction by dividing top and bottom by the GCF.
Worked Examples
One decimal place: 3/10. Already in simplest form. Answer: 3/10.
Two decimal places: 75/100. GCF(75,100) = 25. 75/25 = 3; 100/25 = 4. Answer: 3/4.
Three decimal places: 125/1000. GCF = 125. 125/125 = 1; 1000/125 = 8. Answer: 1/8.
Two decimal places: 6/100. GCF = 2. Answer: 3/50.
Mixed Decimals to Mixed Numbers
Whole part stays: 3. Decimal part: 4/10 = 2/5. Answer: 3 and 2/5 (or 17/5).
2 + 75/100 = 2 + 3/4 = 2 and 3/4 (or 11/4).
Recurring Decimals
Some decimals repeat forever, such as 0.333... = 1/3. These cannot be converted using the place-value method. They require algebra, but they are still exact fractions.
| Recurring Decimal | Fraction |
|---|---|
| 0.333... | 1/3 |
| 0.666... | 2/3 |
| 0.142857... | 1/7 |
| 0.1111... | 1/9 |
Quick Reference
| Decimal | Fraction |
|---|---|
| 0.1 | 1/10 |
| 0.2 | 1/5 |
| 0.25 | 1/4 |
| 0.5 | 1/2 |
| 0.75 | 3/4 |
| 0.8 | 4/5 |
Key Takeaways
- Count decimal places to choose the correct power-of-10 denominator.
- Simplify by dividing both numbers by their GCF.
- Whole-number part stays the same; only the decimal part becomes a fraction.
- Memorise the common decimal-fraction equivalents for speed.
Practice Questions
- Write 0.4 as a fraction in its simplest form.
- Write 0.625 as a fraction.
- Write 1.8 as a mixed number.
- Write 0.048 as a fraction in its simplest form.
- A sprinter's reaction time is 0.15 s. Write this as a fraction of a second.