0.13 Repeating as a Fraction
Have you ever wondered how to convert a repeating decimal into a fraction? In this article, we'll explore how to convert 0.13 repeating into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.13 repeating is a repeating decimal because the digits "13" repeat indefinitely: 0.13131313...
Converting 0.13 Repeating into a Fraction
To convert 0.13 repeating into a fraction, we can use the following steps:
Step 1: Let x = 0.1313...
Let x = 0.1313... (where the dots indicate that the sequence of digits repeats indefinitely).
Step 2: Multiply x by 100
Multiply x by 100 to get:
100x = 13.1313...
Step 3: Subtract x from 100x
Subtract x from 100x to get:
99x = 13
Step 4: Solve for x
Divide both sides of the equation by 99 to get:
x = 13/99
The Answer
So, 0.13 repeating as a fraction is 13/99.
Conclusion
Converting a repeating decimal into a fraction may seem daunting at first, but by following the steps outlined above, you can easily convert any repeating decimal into a fraction. Remember to multiply and subtract to get rid of the repeating part, and then solve for x to get your final answer.
