hkhanexam
Which of the following can be expressed as a repeating decimal in which one of ten digits (other than 0 or 9) is repeated an infinite number of times?
A)1/40
B) 4/75
C) 1/8
D) 17/50
E) 97/100
I got the answer but only by doing it manually... I wonder if anyone knows a quicker way?
The OA in your post is "D", but the right answer here is B.
If, when a fraction of integers is reduced, the only prime divisors of the denominator are 2, 5 or both 2 and 5, then the decimal equivalent of the fraction will always terminate. Since 40, 8, 50 and 100 are all only divisible by 2 and/or 5, the decimal equivalents of A, C, D and E will all terminate (they'll all be finite). Only the decimal of 4/75 will be infinite, because the denominator is divisible by 3.
The wording of the question is very strange - I have no idea what the "one of ten digits" part of the question means.