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Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189

B. 15/196

C. 16/225

D. 25/144

E. 39/128

Ans is E.. it is obvious but I am wondering there is a faster way to solve this one.

My reasoning is

A. 10/189 = 10/(9*21) =

(10/21)(1/9)

since demonominator is multiple of 9, (1/9) is repeating decimal no matter what the value of green, we know blue is repeating decimal. Thus x*repeating decimal = repeating decimal

B. 15/196 = no clue. Is there a short cut??
C. 16/225 = 16/(25*9) = (16/25)*(1/9) => repeating decimal

D. 25/144 = 25/(16*9) = (25/16)*(1/9) => repeating decimal

E. 39/128 = 39/2^7 = obviously terminating decimal.. divided by 2 7times.

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