0.13888 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 0.13888, a repeating decimal, into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of 0.13888, the sequence "88" repeats indefinitely. Repeating decimals can be converted into fractions, and that's what we'll do in this article.
Converting 0.13888 into a Fraction
To convert 0.13888 into a fraction, we can use the following steps:
Step 1: Identify the repeating part
The repeating part of the decimal is "88". Let's call this part "r".
Step 2: Multiply both sides by 100
Multiply both sides of the equation by 100 to get rid of the decimal point:
100x = 13.8888...
Step 3: Subtract the original equation
Subtract the original equation from the new equation:
100x - x = 13.8888... - 0.13888
This simplifies to:
99x = 13.75
Step 4: Divide by 99
Divide both sides by 99 to get the value of x:
x = 13.75 / 99
x = 25/18
So, 0.13888 as a fraction is 25/18.
Conclusion
In this article, we've seen how to convert a repeating decimal, 0.13888, into a fraction. By following the steps outlined above, we were able to convert the decimal into the fraction 25/18. This process can be applied to any repeating decimal to convert it into a fraction.
