0.1212 Repeating as a Fraction
The decimal 0.1212 repeating is a non-terminating, repeating decimal. In this article, we will explore how to convert this repeating decimal into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.1212 repeating, the sequence "12" repeats indefinitely.
Converting a Repeating Decimal to a Fraction
To convert a repeating decimal to a fraction, we can use the following steps:
- Let x = the repeating decimal: In this case, let x = 0.1212.
- Multiply x by 100: This will shift the decimal point two places to the right, so that the repeating sequence starts immediately after the decimal point. This gives us 100x = 12.1212.
- Subtract x from 100x: This will eliminate the repeating sequence, leaving us with a terminating decimal. Subtracting x from 100x gives us 99x = 12.
- Divide by the coefficient of x: In this case, the coefficient of x is 99, so we divide both sides of the equation by 99 to get x = 12/99.
Simplifying the Fraction
The fraction 12/99 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 12 and 99 is 3, so we can divide both numbers by 3 to get:
x = 4/33
Result
Therefore, the repeating decimal 0.1212 is equal to the fraction 4/33.
I hope this article has helped you understand how to convert a repeating decimal to a fraction!
