Question

(a) $\frac{22}{7}$ is a rational number but $\pi$ is an irrational number. Comment on this.

(b) Do the numbers $\frac{1}{3}$ and $\frac{-5}{2}$ lie on the opposite sides of 0 on the number line?

[3 MARKS]

Answer 1

(a) Explanation: 2 Marks
(b) Answer: 1 Mark

(a) $\frac{22}{7}$ is a rational number because we can write it in a form of $\frac{p}{q}$.

The actual value of $\pi$ is 3.141516........which implies that there is no end to the values after the decimal, the decimal goes on forever without repeating.
Hence we are not able to find the actual value of $\pi$ therefore we can't represent it on a number line and moreover, we can't represent it in the form of $\frac{p}{q}$, that's why it is an irrational number.


(b) Yes, the numbers $\frac{1}{3}$ and $\frac{-5}{2}$ lie on the opposite sides of 0 on the number line as one of them is positive and the other is negative.