The decimal expansion of the rational number 14587 / 1250 will termina

1.	The decimal expansion of the rational number 14587 / 1250 will terminate afterA. One decimal placeB. two decimal placeC. three decimal placeD. four decimal place
Answer» Let x = p/q be a rational number, such that the prime factorization of q is of the form 2ⁿ 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 × 5⁴. The maximum power of 2 or 5 in 1250 is 4. So, it will terminate after 4 places of decimals.

The decimal expansion of the rational number 14587 / 1250 will terminate afterA. One decimal placeB. two decimal placeC. three decimal placeD. four decimal place

Answer»

Let x = p/q be a rational number, such that the prime factorization of q is of the form 2ⁿ 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 × 5⁴.

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

So, it will terminate after 4 places of decimals.