Question

How to convert a decimal into a fraction

Answer 1

Converting a decimal into a fraction involves a few straightforward steps. Here’s how you can do it:

### For terminating decimals:
1. **Write down the decimal**: For example, take 0.75.
2. **Count the decimal places**: Determine how many digits are to the right of the decimal point (in this case, 2).
3. **Write the decimal as a fraction**: Place the decimal number over 1 followed by as many zeros as there are decimal places. For 0.75, it becomes \( \frac{75}{100} \).
4. **Simplify the fraction**: Divide both the numerator and denominator by their greatest common divisor (GCD). For 75 and 100, the GCD is 25:
- \( \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \).

### For repeating decimals:
1. **Identify the repeating part**: For example, for 0.666..., identify the repeating digit (6).
2. **Set the decimal as a variable**: Let \( x = 0.666...\).
3. **Multiply by a power of 10**: Multiply by 10 to shift the decimal point over. This gives you \( 10x = 6.666...\).
4. **Subtract the original equation**: Subtract \( x \) from this new equation:
\[
10x - x = 6.666... - 0.666...
\]
This simplifies to \( 9x = 6 \).
5. **Solve for x**: Divide both sides by 9:
\[
x = \frac{6}{9}.
\]
6. **Simplify**: The greatest common divisor of 6 and 9 is 3:
\[
x = \frac{6 \div 3}{9 \div 3} = \frac{2}{3}.
\]

### Summary Example
- **Terminating decimal**: Convert 0.125 to a fraction:
1. Count places (3 decimal places).
2. Write as \( \frac{125}{1000} \).
3. Simplify: \( \frac{125 \div 125}{1000 \div 125} = \frac{1}{8} \).
- **Repeating decimal**: Convert 0.333... to a fraction:
1. Let \( x = 0.333...\).
2. \( 10x = 3.333...\).
3. \( 10x - x = 3 \), so \( 9x = 3 \).
4. Solve \( x = \frac{1}{3} \).

That's how you convert decimals to fractions!