Question 1

Which of the following is a rational number?

Accepted Answer

A rational number is a number that can be expressed in the form $p/q$, where $p$ and $q$ are integers and $q 
eq 0$. Among the given options, $22/7$ is expressed as a ratio of two integers, making it a rational number.

Question 2

Between any two rational numbers, there are:

Accepted Answer

There are infinitely many rational numbers between any two distinct rational numbers. This property is known as the denseness property of rational numbers.

Question 3

Decimal representation of a rational number cannot be:

Accepted Answer

The decimal expansion of a rational number is either terminating or non-terminating recurring. Therefore, it can never be non-terminating non-recurring.

Question 4

The value of $0.\overline{3}$ in the form $p/q$, where $p$ and $q$ are integers and $q 
eq 0$, is:

Accepted Answer

Let $x = 0.333...$ (1). Multiplying by 10, $10x = 3.333...$ (2). Subtracting (1) from (2), we get $9x = 3$, which gives $x = 3/9 = 1/3$.

Question 5

Which of the following is an irrational number?

Accepted Answer

An irrational number cannot be expressed as a simple fraction. $\sqrt{23}$ cannot be simplified to a rational number since 23 is a prime number, making its square root irrational.

Number Systems