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

Answer :

Let x = p/q be a rational number, such that the prime factorization of q is of the form 2^{n} 5^{m}, where n, m are non-negative integers. Then x has a decimal expansion which terminates.

The denominator 1250 can also be written as 2 × 5^{4}.

The maximum power of 2 or 5 in 1250 is 4.

So, it will terminate after 4 places of decimals.

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