Question

State 'T' for true and 'F' for false.
(i) Every rational number can be expressed with a positive numerator.
(ii) $\frac{3}{11}$ cannot be represented as a non-terminating repeating decimal.
(iii) If $\frac{p}{q}$ and $\frac{r}{s}$ are two terminating decimals, then $\frac{p}{q}\times \frac{r}{s}$ is also a terminating decimal.
(iv) If $\frac{p}{q}$ is non-terminating repeating decimal and $\frac{r}{s}$ is a terminating decimal, then ($\frac{p}{q}÷\frac{r}{s}$) is a terminating decimal.

• A. F , T, F , T
• B. T, F, F, T
• C. F , F , F , T
• D. T, F, T, F

Answer 1

Answer: (D)

$\left(i\right)$ Every number can be represented by positive integer. For example $=\frac{5}{(-7)}=\frac{-5}{7}$

$\left(ii\right)$ $\frac{3}{11}$ can be represented as terminating repeating decimal as $0.\overline{27}$.

$\left(iii\right)$ Let two terminating decimals by $\frac{3}{12}$ and $\frac{4}{12}$ then $\frac{3}{12}\times \frac{4}{12}$ is also terminating decimal.

$\left(iv\right)$ Let, $\frac{3}{12}$ and $\frac{1}{3}$ then $\frac{3}{12}\cdot \frac{1}{3}=\frac{1}{12}$ is a also non- terminating decimal.