0.12 Repeating as a Fraction
In mathematics, a repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One such example is 0.12 repeating, which can also be written as 0.1212... . But have you ever wondered what this repeating decimal represents as a fraction?
The Conversion Process
To convert a repeating decimal to a fraction, we can use the following steps:
- Let the repeating decimal be x.
- Multiply x by 10 raised to the power of the number of digits in the repeating pattern.
- Subtract x from the result in step 2.
- Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).
Converting 0.12 Repeating
Let's apply these steps to convert 0.12 repeating to a fraction:
- Let x = 0.1212...
- Multiply x by 10^2 (since the repeating pattern has 2 digits): 100x = 12.1212...
- Subtract x from the result: 100x - x = 12.1212... - 0.1212...
- Simplify the fraction: (12 - 0.12) / (100 - 1) = 12 / 99
The Final Answer
So, 0.12 repeating as a fraction is 12/99, which can be simplified to 4/33.
Remember, this conversion process can be applied to any repeating decimal to find its equivalent fraction representation.
