0.12 Repeating as a Simplified Fraction
Have you ever wondered how to convert a repeating decimal like 0.12 into a simplified fraction? In this article, we will explore the process of converting 0.12 repeating into a simplified fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.12, the digits "12" repeat indefinitely, making it a repeating decimal.
Converting 0.12 Repeating into a Simplified Fraction
To convert 0.12 repeating into a simplified fraction, we can use the following steps:
Step 1: Let x = 0.12 Repeating
Let x = 0.12 where the digits "12" repeat indefinitely.
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
Therefore, 0.12 repeating can be converted into a simplified fraction of 4/33.
Conclusion
In this article, we have learned how to convert a repeating decimal like 0.12 into a simplified fraction. By following the steps outlined above, we can convert any repeating decimal into a simplified fraction.
