Question

After how many places of decimal the decimal expansion of the rational number 47/2^2.5 will terminate?

Answer 1

SOLUTION:
47 /2³× 5²
= 47 ×5/2³× 5² ×5
[Multiply by 5¹ in numerator and denominator]
=47 ×5/2³× 5³
=47 ×5/(2×5)³
=47 ×5/(10)³
=235/1000
=0.235
Hence, the decimal expansion of the rational number 47 /2³× 5² will terminate after 3 places of decimal.

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Answer 2

Solution :

47/( 2² * 5 )

= ( 47 × 5 )/( 2²*5²)

= 235/( 10 )²

= 235/100

= 2.35

Therefore ,

After 2 decimal places 47/( 2²*5 )

terminates .

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