163/150 will have a terminating decimal expansion. state true or false.justify your answer

Answer :

We know if any terminating decimal number represent in fraction than it's denominator will be in form of 2m× 5n .
And

Decimal digits of any number depends on value of m and n , If

We get

m  > n than we get " m " number of decimal digits .
And
If
We get
n  > m than we get " n "  number of decimal digits . 

So,

163150 = 1632× 3 × 5× 5 =16321× 3 × 52

So,

Our denominator is not in form of  2m× 5n .  So
163150  will never have a terminating decimal expansion . 

We can justify it by finding its' value we get

163150  = 1.086666666666666 . . .

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