Which of the following fractions W has a decimal equivalent that is a terminating decimal?
Which of the following fractions W has a decimal equivalent that is a terminating decimal?
Answer/Solution
39/128
Steps/Work
The fraction W will terminate if and only if the denominator has prime divisors only 2 and 5 or both.
A. 10/189 = 10/(3*3*3*7) Non-term.
B. 15/196 = 15/(2*2*7*7) Non-term.
C. 16/225 = 16/(5*5*3*3) Non-term.
D. 25/144 = 25/(2*2*2*7) Non-term.
E. 39/128 = 39/(2^7) Terminatingbecause only 2 in denominator.
A. 10/189 = 10/(3*3*3*7) Non-term.
B. 15/196 = 15/(2*2*7*7) Non-term.
C. 16/225 = 16/(5*5*3*3) Non-term.
D. 25/144 = 25/(2*2*2*7) Non-term.
E. 39/128 = 39/(2^7) Terminatingbecause only 2 in denominator.