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NCERT Solutions Class 9 Mathematics

Exercise 1.1

Q.1. Is zero a rational number? Can you write it in the form $\frac{\mathrm{p}}{\mathrm{q}}$, where p and q are integers and q ≠ 0?

Q.2. Find six rational numbers between 3 and 4.

Q.3. Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$.

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

(i) Every natural number is a whole number.

(ii) Every integer is a whole number.

(iii) Every rational number is a whole number.

NCERT Solutions Class 9 Mathematics

Exercise 1.1

Q.1. Is zero a rational number? Can you write it in the form $\frac{\mathrm{p}}{\mathrm{q}}$, where p and q are integers and q ≠ 0?

Solution:

Yes. Zero is a rational number as it can be represented as $\frac{0}{1}$, $\frac{0}{2}$, etc..

Q.2. Find six rational numbers between 3 and 4.

Solution:

The given numbers can be represented as,

$3=\frac{3}{1}=\frac{3}{1}×\frac{7}{7}=\frac{21}{7}$

$4=\frac{4}{1}=\frac{4}{1}×\frac{7}{7}=\frac{28}{7}$

Therefore, six rational numbers between 3 and 4 are

$\frac{22}{7},\frac{23}{7},\frac{24}{7},\frac{25}{7},\frac{26}{7},\frac{27}{7}.$

Q.3. Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$.

Solution:

The given numbers can be represented as,

$\frac{3}{5}=\frac{3}{5}×\frac{6}{6}=\frac{18}{30}$

$\frac{4}{5}=\frac{4}{5}×\frac{6}{6}=\frac{24}{30}$

Therefore, five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ are

$\frac{19}{30},\frac{20}{30},\frac{21}{30},\frac{22}{30},\frac{23}{30}.$

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

(i) Every natural number is a whole number.

(ii) Every integer is a whole number.

(iii) Every rational number is a whole number.

Solution:

(i) Every natural number is a whole number.

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

(ii) Every integer is a whole number.

• False, as integers may be negative but whole numbers are always positive.

(iii) Every rational number is a whole number.

• False, as rational numbers may be fractional but so they include numbers which are not whole numbers.