# MP Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.1

## MP Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.1

Question 1.
Is zero a rational number? Can vou write it in the form $$\frac{p}{q}$$, where p and q are integers and
q ≠ 0?
Solution:
Yes. 0 can be written as $$\frac{0}{1}$$, $$\frac{0}{2}$$.

Question 2.
Find six rational numbers between 3 and 4.
Solution:
$$\frac{3}{1}$$ and $$\frac{4}{1}$$
Multiplying N and D by 7, we get

Six rational numbers between 3 and 4
= $$\frac{22}{7}$$, $$\frac{23}{7}$$, $$\frac{24}{7}$$, $$\frac{25}{7}$$, $$\frac{26}{7}$$, $$\frac{27}{7}$$

Question 3.
Find five rational numbers between $$\frac{3}{5}$$ and $$\frac{4}{5}$$.
Solution:
$$\frac{3}{5}$$ and $$\frac{4}{5}$$
Multiply N and D by 6, we get,

Five rational numbers between $$\frac{3}{4}$$ and $$\frac{4}{5}$$
= $$\frac{19}{30}$$, $$\frac{20}{30}$$, $$\frac{21}{30}$$, $$\frac{22}{30}$$, $$\frac{23}{30}$$

Question 4.
State whether the following statements are true or false. Give reasons for your answers.

1. Every natural number is a whole number.
2. Every integer is a whole number.
3. Every rational number is a whole number.

Solution:

1. True, every natural number is a whole number.
2. False, because integers also include the negative numbers like – 2, -5 etc., which are not whole numbers.
3. False, because rational numbers are of the form $$\frac{2}{3}$$, $$\frac{0}{1}$$, $$\frac{-3}{2}$$ ….are not whole numbers.

Irrational Number:
Anumber which cannot be expressed in the form $$\frac{p}{q}$$ wherep and q are integers such that q ≠ 0 are called an irrational numbers.
For example: √5, √3, √5 etc.
Also,
A number is an irrational number if it has a non – terminating and non – repeating decimal representation –
√2 = 1.41421…
√3 = 1.73205…