0.12 Recurring as a Fraction in Simplest Form
What is 0.12 Recurring?
0.12 recurring, also written as 0.12..., is a decimal number that has a repeating pattern of 12. This means that the sequence of digits "12" will repeat indefinitely, making it a non-terminating, recurring decimal.
Converting 0.12 Recurring to a Fraction
To convert 0.12 recurring to a fraction, we can use a simple method. Let's assume that the recurring decimal is equal to a variable, x.
x = 0.12...
Since the decimal recurrs every two digits, we can multiply both sides of the equation by 100 to move the decimal point two places to the right.
100x = 12.12...
Now, subtract the original equation from the new equation to eliminate the recurring decimal part.
100x - x = 12.12... - 0.12... 99x = 12
Next, divide both sides of the equation by 99 to solve for x.
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.
x = (12 ÷ 3) / (99 ÷ 3) x = 4/33
The Simplest Form of 0.12 Recurring
Therefore, the simplest form of 0.12 recurring as a fraction is:
4/33
This is the equivalent fraction of the recurring decimal 0.12 in its simplest form.
