Respuesta :
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.
The smallest positive integer n such that n/1260 can be expressed as a terminating decimal is 63
Express 1260 as a product of its prime factors
1260 = 2² x 3² x 5 x 7
Factors of 1260 that do not have terminating decimals will be a factor of the numerator n.
The factors of the 1260 in the given prime factor product that do not have a terminating decimal are 3² and 5
Therefore, n must be at least 3² x 5
n = 9 x 5
n = 63
By testing, 63/1260 = 0.05
Therefore, the smallest positive integer n such that n/1260 can be expressed as a terminating decimal is 63
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