Question

Write whether the rational number 153/1500 will have a terminating decimal expansion or not

Answer 1

Explanation:

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 )

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