0.13 Repeating as a Fraction Simplified
When dealing with decimals, it's often helpful to convert them into fractions. In this article, we'll explore how to convert the repeating decimal 0.13 into a simplified fraction.
What is 0.13 Repeating?
The decimal 0.13 is a repeating decimal because it goes on indefinitely in a pattern. In this case, the pattern is 13, so the decimal can be written as 0.131313...
Converting 0.13 Repeating into a Fraction
To convert 0.13 into a fraction, we can use the following steps:
Step 1: Let x = 0.131313...
Let's assign the variable x to the repeating decimal 0.131313....
Step 2: Multiply Both Sides by 100
Multiply both sides of the equation by 100 to get rid of the decimal point:
100x = 13.131313...
Step 3: Subtract x from Both Sides
Subtract x from both sides of the equation to get:
99x = 13
Step 4: Divide Both Sides by 99
Divide both sides of the equation by 99 to solve for x:
x = 13/99
Simplifying the Fraction
The fraction 13/99 is already in its simplest form, so we don't need to simplify it further.
Conclusion
In conclusion, the repeating decimal 0.13 can be converted into a simplified fraction as follows:
0.13 = 13/99
This article has shown the step-by-step process of converting a repeating decimal into a simplified fraction. This skill is useful in various mathematical applications and can help you solve problems more efficiently.
