0.12 Recurring as a Fraction in its Simplest Form
What is 0.12 recurring?
0.12 recurring, also known as 0.121212..., is a non-terminating decimal that repeats infinitely. This type of decimal is also known as a repeating decimal or a recurring decimal.
Converting 0.12 Recurring to a Fraction
To convert 0.12 recurring to a fraction, we can use the following steps:
Step 1: Let x = 0.121212...
Step 2: Multiply both sides of the equation by 100 to remove the decimal places.
100x = 12.121212...
Step 3: Subtract x from both sides of the equation to eliminate the repeating part.
99x = 12
Step 4: 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
Final Answer
Therefore, 0.12 recurring as a fraction in its simplest form is:
4/33
This is the simplest form of the fraction, and it is equivalent to the original decimal 0.12 recurring.
