Exercise 1.1

Is zero a rational number? Can you write it in the form and q ≠ 0?

Instruction

Is zero a rational number:

To show that zero is a rational number, you can write it as : / that is equal to .

Therefore, zero can be written as a fraction with a non-zero denominator, making it a rational number.

Find six rational numbers between 3 and 4.

Instruction

3 and 4

As we have to find 6 rational numbers in between 3 and 4, let change the form of 3 and 4. Let's multiply both the numbers by say, 77.
For 3: 3 × 77 = .
For 4: 4 × 77 = .
Now, we can write six rational numbers that lie between 3 and 4 i.e. between 21/7 and 28/7.
Rational Numbers between 3 and 4: , ,,, and .
We have found six rational numbers that lie between 3 and 4.

Find five rational numbers between 35 and 45.

Instruction

3/5 and 4/5

As we have to find 5 rational numbers in between 35 and 45, let's change its form. Let's multiply both the numbers by say, 66.
For 35: 35 × 66 = .
For 45: 45 × 66 = .
Now, we get 5 rational numbers between 35 and 45 i.e. from 1830 to 2430.
Five Rational Numbers: , ,, and .
We have found five rational numbers that lie between 35 and 45.

State whether the following statements are true or false. Give reasons for your answers.

(i) Every natural number is a whole number : .

Reasoning: Natural numbers are the set of positive integers starting from 1,... Whole numbers include all natural numbers and the number 0,....

(ii) Every integer is a whole number : .

Reasoning: Integers include all positive and negative whole numbers, as well as zero.Whole numbers are only non-negative integers.

(iii) Every rational number is a whole number : .

Reasoning: Rational numbers are numbers that can be expressed as a fraction p/q where p and q are integers and q ≠ 0.

Number Systems