0.12 Repeating as a Fraction in Simplest Form
In mathematics, repeating decimals can be converted into fractions. One such repeating decimal is 0.12, which repeats indefinitely. In this article, we will explore how to convert 0.12 repeating into a fraction in its simplest form.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.12, 0.1234, and 0.5678 are all repeating decimals.
Converting 0.12 Repeating to a Fraction
To convert 0.12 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.12
Let's say x = 0.12, where x is a variable.
Step 2: Multiply both sides by 100
Multiply both sides of the equation by 100 to get:
100x = 12.12
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
99x = 12
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to get:
x = 12/99
Step 5: Simplify the fraction
Simplify the fraction 12/99 by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
x = 4/33
So, 0.12 Repeating as a Fraction in Simplest Form is:
4/33
In conclusion, 0.12 repeating can be converted into a fraction in its simplest form as 4/33. This process can be applied to any repeating decimal to convert it into a fraction.
