2. Without actually performing the long division, find ifwill have ter

1.	2. Without actually performing the long division, find ifwill have terminat ing or non-10500terminating (repeating) decimal expansion. Give reasons for your answer.
Answer» 987 = 3 × 7 × 47 10500 = 2 × 2 × 3 × 5 × 5 × 5 × 7 HCF of 987 and 10500 = 3 × 7 = 21 Therefore , Least form of the fraction = 987 / 10500 Divide numerator and denominator with HCF, we get, = ( 987 / 21 ) / ( 10500 / 21 ) = 47 / 500 987 / 10500 = 47 / 500 Denominator = 500 = 2^2 × 5^2 We have only 2 and 5 as factors . Therefore , 987 / 10500 is terminating decimal.

2. Without actually performing the long division, find ifwill have terminat ing or non-10500terminating (repeating) decimal expansion. Give reasons for your answer.

Answer»

987 = 3 × 7 × 47

10500 = 2 × 2 × 3 × 5 × 5 × 5 × 7

HCF of 987 and 10500 = 3 × 7 = 21

Therefore ,

Least form of the fraction = 987 / 10500

Divide numerator and denominator with HCF,

we get,

= ( 987 / 21 ) / ( 10500 / 21 )

= 47 / 500

987 / 10500 = 47 / 500

Denominator = 500

= 2^2 × 5^2

We have only 2 and 5 as factors .

Therefore ,

987 / 10500 is terminating decimal.