Q. 144.1( 16 Votes )
The decimal expansion of the rational number 14587 / 1250 will terminate after
A. One decimal place
B. two decimal place
C. three decimal place
D. four decimal place
Let x = p/q be a rational number, such that the prime factorization of q is of the form 2n 5m, where n, m are non-negative integers. Then x has a decimal expansion which terminates.
The denominator 1250 can also be written as 2 × 54.
The maximum power of 2 or 5 in 1250 is 4.
So, it will terminate after 4 places of decimals.
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