Converting 0.08 8 Repeating to a Fraction
Have you ever wondered how to convert a repeating decimal into a fraction? In this article, we will explore the process of converting 0.08 8 repeating to a fraction.
Understanding Repeating Decimals
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.08 8 repeating, the sequence "08" repeats indefinitely.
Converting to a Fraction
To convert a repeating decimal to a fraction, we can use the following steps:
Step 1: Identify the repeating part
In this case, the repeating part is "08".
Step 2: Let x be the repeating decimal
Let x = 0.08 8 repeating.
Step 3: Multiply x by 100
Multiplying x by 100 gives us:
100x = 8.08 8 repeating
Step 4: Subtract x from 100x
Subtracting x from 100x gives us:
99x = 8
Step 5: Divide by 99
Dividing both sides by 99 gives us:
x = 8/99
Result
Therefore, 0.08 8 repeating can be converted to the fraction:
8/99
This fraction is in its simplest form, and it represents the same value as the repeating decimal 0.08 8 repeating.
Conclusion
Converting repeating decimals to fractions can be a useful skill in mathematics. By following the steps outlined above, we can convert any repeating decimal to a fraction. In this case, we converted 0.08 8 repeating to the fraction 8/99.
