51Has the rational number 1500 a terminating or non terminating decima

1.	51Has the rational number 1500 a terminating or non terminating decimalexpansion? (CBSE 2009-1M)
Answer» If a fraction , in its lowest terms , denominator has no other prime factors except 2 and 5 it can be expressed as a terminating decimal. First we have write 51 / 1500 in it's least form 51 / 1500 = ( 3 × 17 ) / ( 3 × 500 ) After cancellation , we get 51 / 1500 = 17 / 500 denominator = 500 = 2 × 2 × 5 × 5 × 5 Therefore , The denominator has no other prime factors except 2 and 5 . 51 / 1500 is terminating decimal. 51 / 1500 = 17 / ( 2^2 × 5^3 ) = ( 17 × 2 ) / ( 2^3 × 5^3 ) = 34 / ( 2 ^3 × 5^3 ) = 0.034 ( terminating decimal )

51Has the rational number 1500 a terminating or non terminating decimalexpansion? (CBSE 2009-1M)

Answer»

If a fraction , in its lowest terms , denominator

has no other prime factors except 2 and 5

it can be expressed as a terminating

decimal.

First we have write 51 / 1500 in it's

least form

51 / 1500 = ( 3 × 17 ) / ( 3 × 500 )

After cancellation , we get

51 / 1500 = 17 / 500

denominator = 500

= 2 × 2 × 5 × 5 × 5

Therefore ,

The denominator has no other

prime factors except 2 and 5 .

51 / 1500 is terminating decimal.

51 / 1500 = 17 / ( 2^2 × 5^3 )

= ( 17 × 2 ) / ( 2^3 × 5^3 )

= 34 / ( 2 ^3 × 5^3 )

= 0.034 ( terminating decimal )