Question

Assertion: 0.7 is a rational number between 0.5 and 0.9.

Reason: A rational number between a and b is `(a + b)/3`.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

Assertion (A) is true but Reason (R) is false.

Explanation:

Assertion (A): 0.7 is a rational number between 0.5 and 0.9. This is true because 0.7 is a terminating decimal, which can be expressed as the fraction `7/10`, so it is rational and lies between 0.5 and 0.9.

Reason (R): A rational number between a and b is `(a + b)/3`. This is false. The rational number between a and b is generally given by `(a + b)/2` the midpoint, not `(a + b)/3`.

Thus, the assertion is correct, but the reason is an incorrect statement about how to find a rational number between two numbers.