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
MP Board Class 9th Maths Chapter 1 Number Systems Ex 1.1 1
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,
MP Board Class 9th Maths Chapter 1 Number Systems Ex 1.1 3
Five rational numbers between \(\frac{3}{4}\) and \(\frac{4}{5}\)
= \(\frac{19}{30}\), \(\frac{20}{30}\), \(\frac{21}{30}\), \(\frac{22}{30}\), \(\frac{23}{30}\)

MP Board Solutions

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…

MP Board Class 9th Maths Solutions