Question

1. Assertion: denominator of 12.145. when expressed in the form ofp/q, q=0 is of the form 2m×5n, where m and n are non-negative integers. Reason : 12.145 is a terminating decimal fraction

A) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

B) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.

C) Assertion is correct but Reason is incorrect.

D) Assertion is incorrect but Reason is correct.​

Answer 1

Answer:

Correct option isA

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

In a fraction, if the denominator is of the form 2

n ×5 m then the fraction is always terminating.

In this case, 34.12345= 1000003412345

Denominator is 100000=10

5=2 5×5 5

Denominator is of the form 2 n×5 m

So, it is terminating and reason is the correct explanation to assertion.

Option A

Answer 2

Given : Assertion: denominator of 12.145. when expressed in the form of p/q, q=0 is of the form 2^m×5^n, where m and n are non-negative integers. Reason : 12.145 is a terminating decimal fraction

To Find : Comment on Assertion and Reason

Solution:

All real numbers which can be expressed in p/q form where p and q are integers and q ≠ 0 are rational numbers

Rational numbers in which numerator and denominators are co prime and denominators can be written in the form  $2^m.5^n$  where m and n are non negative integers are  Terminating decimals

and others are non terminating recurring decimals

Assertion: denominator of 12.145. when expressed in the form of p/q, q=0 is of the form 2^m×5^n, where m and n are non-negative integers.

12.145

= 12145/1000

= 2429/200

= 2429/2³ * 5²

Hence  Assertion is True

Reason : 12.145 is a terminating decimal fraction  

TRUE

Correct option is  A

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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