0.12 Repeating as a Fraction
What is 0.12 Repeating?
0.12 repeating is a decimal number that has a repeating pattern of digits. In this case, the digits "12" repeat infinitely. This type of decimal is also known as a repeating decimal or recurring decimal.
Converting 0.12 Repeating to a Fraction
To convert 0.12 repeating to a fraction, we need to find the equivalent fraction that represents the same value.
Let's call the repeating decimal x:
x = 0.121212...
We can multiply both sides of the equation by 100, which is the same as shifting the decimal point two places to the right:
100x = 12.121212...
Now, subtract the original equation from the new equation:
100x - x = 12.121212... - 0.121212...
This simplifies to:
99x = 12
Divide both sides by 99:
x = 12/99
We can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3:
x = 4/33
So, 0.12 Repeating as a Fraction is:
4/33
This fraction represents the same value as the repeating decimal 0.12.
