0.017 Recurring as a Fraction
What is 0.017 recurring?
0.017 recurring, also known as 0.017~, is a repeating decimal. It's a decimal that has a finite number of digits that repeat indefinitely in a sequence. In this case, the repeating part is "017".
Converting 0.017 recurring to a fraction
To convert 0.017 recurring to a fraction, we can use the following steps:
Step 1: Let x = 0.017~
Let's assume that x = 0.017~.
Step 2: Multiply x by 1000
Multiply both sides of the equation by 1000 to get rid of the decimal places.
1000x = 17.017~
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to eliminate the x term.
999x = 17
Step 4: Divide both sides by 999
Divide both sides of the equation by 999 to solve for x.
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, which is 1.
x = 17/999
Therefore, 0.017 recurring as a fraction is equal to 17/999.
Conclusion
In conclusion, we have successfully converted 0.017 recurring to a fraction, which is 17/999. This process can be applied to any repeating decimal to convert it to a fraction.
