Question

S1 : $\frac{1323}{1400}$ is a non terminating decimal.
S2 : A number $\frac{p}{q}$ where p and q are co-primes is terminating if q is of the form $2^n{.3}^m$ where n and m are non-negative integers.

• A. S1 and S2 are true.
• B. S1 and S2 are false
• C. S1 is false and S2 is true
• D. S1 is true and S2 is false

Answer 1

The correct option is D

S1 is true and S2 is false

1400 = $2^3\times 5^2\times 7$
$\Rightarrow$ The denominator is not in the form of $2^n{5}^m$.
Therefore, the given rational number has non- terminating decimal expansion.
Hence, S1 is true.

A number $\frac{p}{q}$ where p and q are co-primes is terminating if q is of the form $2^m{.5}^n$.
Hence S2 is false.

The second statement is correct.