To convert the repeating decimal 0.015 into a fraction, let’s designate it as x:
x = 0.015151515… (where ’15’ repeats).
Next, we can eliminate the repeating part by multiplying x by 1000, which moves the decimal point three places to the right:
1000x = 15.151515…
Now, we can set up another equation by multiplying x by 10:
10x = 0.151515…
Next, we subtract the second equation from the first:
1000x – 10x = 15.151515… – 0.151515…
990x = 15
Now, we can solve for x:
x = 15 / 990
Finally, we can simplify this fraction. The GCD (greatest common divisor) of 15 and 990 is 15.
Dividing the numerator and the denominator by 15 gives us:
x = 1 / 66
Thus, 0.015 repeating as a fraction is 1/66.