Question

Without actual division check after how many decimal places 27/ 1250will terminate?

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Answer 1

Answer:

Step-by-step explanation:

Hi ,

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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.

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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.

Answer 2

Answer:terminate

Step-by-step explanation:

1250=2×5×5×5×5

1250=2^1×5^4

Since,1250 can be of form 2^m × 5^m

So,27/1250 will terminate