0.17 Repeating as a Fraction in Simplest Form
Introduction
Repeating decimals can be rewritten as fractions in simplest form. In this article, we will explore how to convert the repeating decimal 0.17 to a fraction in its simplest form.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.17 is a repeating decimal because the sequence "17" repeats indefinitely: 0.171717...
Converting 0.17 to a Fraction
To convert 0.17 to a fraction, we can use the following steps:
Step 1: Let x = 0.17
Let's say x = 0.17.
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 17.17
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
99x = 17
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to get:
x = 17/99
Simplify the Fraction
The fraction 17/99 is already in its simplest form.
Answer
Therefore, 0.17 as a fraction in simplest form is 17/99.
Conclusion
In this article, we have learned how to convert the repeating decimal 0.17 to a fraction in its simplest form. By following the steps outlined above, we can convert any repeating decimal to a fraction in its simplest form.
