Converting Between Common Fractions and Decimals
Key Idea
Common fractions and decimals are two different ways to write the same value! Every decimal can be written as a common fraction, but not every common fraction gives an exact decimal.
Part 1: Decimal → Common Fraction
The Method:
- Write the digits after the decimal point as the numerator
- The denominator is a power of 10 based on decimal places
- Simplify the fraction by finding the GCD
| Decimal Places | Denominator | Example |
|---|---|---|
| 1 place | 10 | 0.7 = 7/10 |
| 2 places | 100 | 0.25 = 25/100 = 1/4 |
| 3 places | 1000 | 0.125 = 125/1000 = 1/8 |
Simplifying After Conversion
Always find the Greatest Common Divisor (GCD) and reduce:
- 0.25 = 25/100 → GCD(25,100)=25 → 1/4
- 0.5 = 5/10 → GCD(5,10)=5 → 1/2
- 0.75 = 75/100 → GCD(75,100)=25 → 3/4
Part 2: Common Fraction → Decimal
Method 1: Division (Universal)
Divide the numerator by the denominator:
3/4 = 3 ÷ 4 = 0.75
1/8 = 1 ÷ 8 = 0.125
5/8 = 5 ÷ 8 = 0.625
Method 2: Equivalent Fraction
Make the denominator 10, 100, or 1000:
1/2 = 5/10 = 0.5
3/4 = 75/100 = 0.75
1/5 = 2/10 = 0.2
This method only works when the denominator can become a power of 10!
Which Fractions Give Exact Decimals?
YES - Exact Decimals
Fractions whose denominator (in lowest terms) has only factors of 2 and/or 5:
1/2, 1/4, 1/5, 1/8, 1/10, 1/20, 1/25, 1/40, 1/50
NO - Repeating Decimals
Fractions with other prime factors in the denominator:
1/3, 1/6, 1/7, 1/9, 1/11, 1/12, 1/13
Interactive visualization — available in the full lesson