Question

Write the decimal expansion of 27 by 1250 without actual division

Answer 1

Step-by-step explanation:

Let x = p / q be a rational number

such that the prime factorization of

' q ' is of the form 2^n5^m , where

n , m are non - negative integers.

Then ' x ' has a deciamal expansion

which terminates.

___________________________

According to the given problem,

27 / 1250

= 27/ ( 2 × 5^4)

= ( 27 × 2^3 )/ ( 2 × 2^3 × 5^4 )

= 216/ ( 2^4 × 5^4 )

Denominator = q is in the form of

2^n5^m

= 216/ ( 10)^4

= 0.0216 is a terminating decimal.

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