## 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.

- Every natural number is a whole number.
- Every integer is a whole number.
- Every rational number is a whole number.

Solution:

- True, every natural number is a whole number.
- False, because integers also include the negative numbers like – 2, -5 etc., which are not whole numbers.
- 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…