0.17 Repeating as a Fraction
Introduction
Have you ever wondered how to convert a repeating decimal into a fraction? In this article, we will explore how to convert 0.17 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, 0.17 repeating can be written as 0.171717... where the sequence "17" repeats indefinitely.
Converting 0.17 Repeating into a Fraction
To convert 0.17 repeating into a fraction, we can use the following steps:
Step 1: Let x = 0.17 Repeating
Let x = 0.171717...
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 17.1717...
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
Therefore, 0.17 repeating can be written as a fraction as:
17/99
Conclusion
In this article, we have successfully converted 0.17 repeating into a fraction. By following the steps outlined above, you can convert any repeating decimal into a fraction. Remember to multiply by the appropriate power of 10, subtract the original decimal, and solve for x to get the equivalent fraction.
