0.116 Repeating as a Fraction
What is 0.116 Repeating?
0.116 repeating, also known as 0.116..., is a non-terminating repeating decimal. This means that the decimal representation of the number goes on indefinitely in a repeating pattern.
Converting 0.116 Repeating to a Fraction
To convert 0.116 repeating to a fraction, we can use the following steps:
- Let x = 0.116...
- Multiply both sides by 1000 to get 1000x = 116.116...
- Subtract x from both sides to get 999x = 116
- Divide both sides by 999 to get x = 116/999
Simplifying the Fraction
The resulting fraction, 116/999, can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
GCD of 116 and 999
The GCD of 116 and 999 is 1, which means that the fraction is already in its simplest form.
Final Answer
Therefore, 0.116 repeating as a fraction is 116/999.
Conclusion
In this article, we have successfully converted the non-terminating repeating decimal 0.116... to a fraction, which is 116/999. This process can be applied to other repeating decimals as well, making it a useful tool in mathematics.
