.11111 Repeating as a Fraction
How to write .11111 Repeating as a Fraction? To convert a repeating decimal to a fraction, you set up an equation where the repeating decimal equals a variable, multiply to shift the repeating part, subtract to eliminate the repeating part, and solve for the variable.
Step-by-Step Calculation:
What is .11111 Repeating as a Fraction?
.11111 (repeating) Decimal = 1/9 as a Fraction
How to Convert Repeating Decimal to Fraction
To convert a repeating decimal number to a fraction, follow these steps:
- Regular Decimals: Count decimal places, write as fraction with denominator as power of 10, then simplify.
- Repeating Decimals: Use algebraic method - multiply by powers of 10 to align repeating parts, then subtract to eliminate repetition.
- Simplification: Find the Greatest Common Divisor (GCD) and divide both numerator and denominator by it.
Repeating Decimal to Fraction Conversion Examples
Here are some examples of repeating decimal numbers converted to fractions:
| Repeating Decimal | as a Fraction |
|---|---|
| 0.11106 (5) | 1234/11111 |
| 0.11107 (5) | 11107/99999 |
| 0.11108 (5) | 11108/99999 |
| 0.11109 (5) | 3703/33333 |
| 0.1111 (4) | 1/9 |
| 0.11111 (5) | 1/9 |
| 0.11112 (5) | 3704/33333 |
| 0.11113 (5) | 11113/99999 |
| 0.11114 (5) | 11114/99999 |
| 0.11115 (5) | 1235/11111 |
| 0.11116 (5) | 11116/99999 |
Conclusion
Converting decimals to fractions is a useful skill in mathematics. Whether dealing with regular or repeating decimals, the methods outlined above provide a clear path to expressing decimals as fractions. Practice with various decimal numbers to become proficient in these conversion techniques.