Question

1. The rational number 54/343 will have :
(a) terminating decimal expansion
(b) terminating, repeating decimal
expansion
(c) non-terminating, repeating decimal
expansion
(d) non-terminating, non-repeating
decimal expansion​

Answer 1

Answer:

This number will have a non-terminating, non-repeating decimal expansion

Option: d

Answer 2

Option (d) non-terminating, non-repeating decimal expansion.

Given

To choose the correct option from the given question.

Given rational number is 54/343.

Rational numbers are in the form of P/Q.

To check whether the rational number is terminating follow the steps given below :

(a) Check whether P and Q are co-prime or not.      

(b) Q must be in the form of $2^n$ $5^m$.

Verification :

(a) Checking whether P and Q are co-prime or not :

     P = 29 = 29×1

     Q = 343 = 7×7×7

They don't have common factor, hence it is a co-prime.

(b) Verifying whether the Q must be in the form of $2^n$ $5^m$ :

     Q = 343 = 7³

Hence, they are not in the form of  $2^n$ $5^m$. So, its not a terminating decimal.      

Therefore, option (d) is the correct answer.  

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