Exercise 1.1

Q1. Is zero a rational number? Can you write it in the form of `frac{p}{q}`: where p and q are integers and q≠0.
Ans. :

Yes,

`0` =`frac{0}{1}`=`frac{0}{2}`= `frac{0}{3}` etc.,

denominator q can also be taken as a negative integer.

Q2. Find six rational numbers between 3 and 4.
Sol.

The denominator of these rational number will 6+1 = 7,

We can write given numbers 3 and 4 in `frac{p}{q}` form where q ≠ 0.

`frac{3×7}{1×7}` =`frac{21}{7}`

and

`frac{4×7}{1×7}` = `frac{28}{7}`

So that required 6 rational numbers are:

`frac{22}{7}`, `frac{23}{7}`, `frac{24}{7}`, `frac{25}{7}`, `frac{26}{7}`, `frac{27}{7}`

Answer :

`frac{22}{7}`, `frac{23}{7}`, `frac{24}{7}`, `frac{25}{7}`, `frac{26}{7}`, `frac{27}{7}`

Q3. Find five rational numbers between `frac{3}{5}` and `frac{4}{5}`
Sol:

We find five rational number between `frac{3}{5}` and `frac{4}{5}`
So we multiply numerator and denominator by (5+1) = 6

`frac{3×6}{5×6}` = `frac{18}{30}`

and

`frac{4×6}{5×6}` = `frac{20}{30}`

So that required 5 rational numbers are:
`frac{19}{30}`, `frac{20}{30}`, `frac{21}{30}`, `frac{22}{30}`, `frac{23}{30}`

Answer :

`frac{19}{30}`, `frac{20}{30}`, `frac{21}{30}`, `frac{22}{30}`, `frac{23}{30}`

Q4. State whether the following statements are true or false. Give reasons for your answer :

(i) Every natural number is a whole number.

Answer :

True, since the collection of whole numbers contains all the natural numbers.

(ii) Every integer is a whole number.

Answer :

False, for example, -2 is not a whole number.

(iii) Every rational number is a whole number.

Answer :

False, for example, `frac{1}{2}` is a rational number but not a whole number.

NCERT Class 9th solution of Exercise 1.2