Write the decimal expansion of 27 by 1250 without actual division
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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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