0.017 Repeating as a Fraction
The decimal 0.017 is a repeating decimal, and in this article, we will explore how to convert it 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 0.017, the sequence "017" repeats indefinitely, making it a repeating decimal.
Converting 0.017 into a Fraction
To convert 0.017 into a fraction, we can use the following steps:
Step 1: Let x = 0.017
Let's assume that x = 0.017. We want to find the fraction equivalent of x.
Step 2: Multiply x by 1000
Multiply both sides of the equation by 1000 to get:
1000x = 17.017
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
999x = 17
Step 4: Divide both sides by 999
Divide both sides of the equation by 999 to get:
x = 17/999
Step 5: Simplify the fraction
The fraction 17/999 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1 in this case. Therefore, the simplified fraction is:
x = 17/999
Result
The repeating decimal 0.017 is equivalent to the fraction 17/999.
Conclusion
In this article, we have successfully converted the repeating decimal 0.017 into a fraction. The technique used is a common method for converting repeating decimals into fractions. By following these steps, you can convert any repeating decimal into a fraction.
