0.1313 Repeating as a Fraction
Introduction
Repeating decimals are a fascinating topic in mathematics, and one common example is 0.1313 repeating. In this article, we will explore how to convert this repeating decimal into a 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 0.1313 repeating, the sequence "13" repeats indefinitely.
Converting 0.1313 Repeating to a Fraction
To convert 0.1313 repeating to a fraction, we can use a clever trick. Let's assume that the repeating decimal is equal to a variable, say x.
x = 0.1313...
We can multiply both sides of the equation by 100 to get:
100x = 13.1313...
Now, subtract the original equation from the new equation:
100x - x = 13.1313... - 0.1313...
This simplifies to:
99x = 13
Now, divide both sides by 99:
x = 13/99
So, the repeating decimal 0.1313 repeating is equal to the fraction 13/99.
Conclusion
In conclusion, we have successfully converted the repeating decimal 0.1313 repeating to a fraction, which is 13/99. This technique can be applied to any repeating decimal to convert it into a fraction.
