0.12 Repeating Decimal as a Fraction
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In this article, we will explore how to convert the repeating decimal 0.12 to a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.12341234... is a repeating decimal because the sequence "1234" repeats indefinitely.
How to Convert 0.12 Repeating Decimal to a Fraction
To convert 0.12 repeating decimal to a fraction, we can use the following steps:
Step 1: Let x = 0.12...
Let x = 0.12... be the repeating decimal.
Step 2: Multiply x by 100
Multiply x by 100 to get:
100x = 12.12...
Step 3: Subtract x from 100x
Subtract x from 100x to get:
99x = 12
Step 4: Divide by 99
Divide both sides by 99 to get:
x = 12/99
Step 5: Simplify the Fraction
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 12 and 99 is 3.
x = 4/33
Therefore, the repeating decimal 0.12... is equal to the fraction 4/33.
Conclusion
In conclusion, we have successfully converted the repeating decimal 0.12... to a fraction, which is 4/33. This method can be applied to any repeating decimal to convert it to a fraction.
