What is the smallest positive integer n such that n/1260 can be expressed as a terminating decimal?
Question
Answer:
1260=2²×3²×5×7 so, since 2ˣand 5ˣ have terminating decimals for integer x, but 3² and 7 do not, the numerator must contain these factors. The smallest value for n is 3²×7=63, so 63/1260 is the expression=1/20=0.05. Answer n=63.
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