0.17 Recurring as a Fraction
Have you ever wondered how to convert a recurring decimal into a fraction? In this article, we will explore how to convert 0.17 recurring into a fraction.
What is a Recurring Decimal?
A recurring decimal, also known as a repeating decimal, is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.17 recurring can be written as 0.1717171717... where the sequence "17" repeats indefinitely.
Converting 0.17 Recurring into a Fraction
To convert 0.17 recurring into a fraction, we can use the following steps:
Step 1: Let x = 0.171717...
Let x = 0.171717... represent the recurring decimal.
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 17.171717...
Step 3: Subtract x from 100x
Subtract x from both sides of the equation to get:
99x = 17
Step 4: Solve for x
Divide both sides of the equation by 99 to get:
x = 17/99
Result
Therefore, 0.17 recurring can be converted into the fraction 17/99.
Conclusion
In conclusion, we have successfully converted 0.17 recurring into a fraction, which is 17/99. This method can be applied to convert any recurring decimal into a fraction.
