9514 1404 393
Answer:
20
Step-by-step explanation:
An equivalent decimal fraction is non-repeating if and only if the fraction denominator has a prime factorization consisting only of powers of 2 and 5.
Powers of 2 less than 300 are ...
2, 4, 8, 16, 32, 64, 128, 256
Powers of 5 less than 300 are ...
5, 25, 125
A fraction will have a finite decimal representation if its denominator is one of these numbers, or some product of these numbers.
Products would include ...
10, 50, 250, 20, 100, 40, 200, 80, 160
The count of all of the listed numbers is ...
8 powers of 2 + 3 powers of 5 + 9 powers of 2 and 5 = 20 listed numbers
There are 20 finite decimal fractions among the fractions 1/2 ... 1/300.
