0.1 Repeating Decimal as a Fraction
What is 0.1 Repeating Decimal?
The decimal number 0.1 repeating, also known as 0.111..., is a non-terminating and non-repeating decimal that goes on indefinitely. It is a recurring decimal, meaning that the sequence of digits repeats in a cycle.
Converting 0.1 Repeating Decimal to a Fraction
To convert 0.1 repeating decimal to a fraction, we can use the following steps:
- Let x = 0.1 repeating: We can start by letting x = 0.1 repeating.
- Multiply x by 10: Multiply both sides of the equation by 10 to get 10x = 1.1 repeating.
- Subtract x from 10x: Subtract x from both sides of the equation to get 9x = 1.
- Divide by 9: Divide both sides of the equation by 9 to get x = 1/9.
Therefore, 0.1 repeating decimal is equal to 1/9 as a fraction.
Why Does This Work?
The reason this method works is because the repeating decimal 0.1 repeating can be thought of as an infinite geometric series. When we multiply x by 10, we are essentially shifting the decimal one place to the right. By subtracting x from 10x, we are effectively subtracting the original decimal from the shifted decimal, leaving us with a remainder of 1.
Conclusion
In conclusion, the 0.1 repeating decimal is equal to 1/9 as a fraction. This conversion is possible through a simple algebraic manipulation of the decimal, allowing us to express the repeating decimal as a simple fraction.
