Question

A rational number m is described below.
m=Prime number/15
Consider the following conclusions about the number m.
Conclusion 1: The decimal expansion of m is non-terminating recurring but the decimal expansion of 3m is
terminating
Conclusion 2. The decimal expansion of m is terminating.
Which of these is correct?
a. Conclusion I is valid but Conclusion 2 is valid only for the prime number 3.
b. Conclusion I is valid but Conclusion 2 is valid only for the prime number 5.
Conclusion 1 is not valid but Conclusion 2 is valid only for the prime number 3.
d. Conclusion 1 is not valid but Conclusion 2 is valid only for the prime number 5.​

Answer 1

Given : A rational number m is described below.   m=Prime number/15  

Conclusion 1: The decimal expansion of m is non-terminating recurring but the decimal expansion of 3m is  terminating

Conclusion 2. The decimal expansion of m is terminating.

To Find : Which of these is correct?

a. Conclusion I is valid but Conclusion 2 is valid only for the prime number 3.

b. Conclusion I is valid but Conclusion 2 is valid only for the prime number 5.

Conclusion 1 is not valid but Conclusion 2 is valid only for the prime number 3.

d. Conclusion 1 is not valid but Conclusion 2 is valid only for the prime number 5.​

Solution:

m=Prime number/15

The decimal expansion of m is non-terminating recurring  - Valid  except for Prime number 3

as for prime number 3   m = 3/15  = 1/5 = 0.2

decimal expansion of 3m is  terminating  Valid   as 3m = 3k/15 = k/5  

Hence conclusion 1 is not completely  Valid

Conclusion 2. The decimal expansion of m is terminating.  Not Valid

as its valid only for prime number 3

Correct Statement :

Conclusion 1 is not valid but Conclusion 2 is valid only for the prime number 3.

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