# Number System class 9 exercise 1.1

NCERT solution for MATHS class 9 NUMBER SYSTEM chapter 1 Exercise-1.1

1. Is zero a rational number? Can you write it in the form p/q, where p and q are integers and q ≠ 0?

Earlier, We know that a number is said to be rational if it can be written in the form p/q, where p and q are integers and q ≠ 0.

Taking the case of ‘0’,

similarly, Zero can be written in the form 0/1, 0/2, 0/3 …

Then, it satisfies the necessary condition, we can conclude that the number (zero) 0 can be written in the p/q form, where q can either be a positive or negative number.

Hence, 0 is a rational number.

2. In short find six rational numbers between 3 and 4.

x_1=\frac{3+4}{2}=\frac{7}{2};3<\frac{7}{2}<4
x_2=\frac{3+\frac{7}{2}}{2}=\frac{13/2}{2}=\frac{13}{4};3<\frac{13}{4}<\frac{7}{2}<4
x_3=\frac{4+\frac{7}{2}}{2}=\frac{15/2}{2}=\frac{15}{4};3<\frac{13}{4}<\frac{7}{2}<\frac{15}{4}<4
x_4=\frac{\frac{7}{2}+\frac{13}{4}}{2}=\frac{\frac{7*2+13}{4}}{2}=\frac{27}{8};3<\frac{13}{4}<\frac{27}{8}<\frac{7}{2}<\frac{15}{4}<4
x_5=\frac{1}{2}\times(\frac{7}{2}+\frac{15}{4})=\frac{1}{2}\times(\frac{14+15}{4})=\frac{29}{8};~~~3<\frac{13}{4}<\frac{27}{8}<\frac{7}{2}<\frac{29}{8}<\frac{15}{4}<4
x_6=\frac{1}{2}\times(\frac{13}{4}+\frac{27}{8})=\frac{1}{2}\times(\frac{26+27}{8})=\frac{29}{16};3<\frac{13}{4}<\frac{53}{16}<\frac{27}{8}<\frac{7}{2}<\frac{29}{8}<\frac{15}{4}<4

## 3. In short find five rational numbers between 3/5 and 4/5.

Trick: if we need to find ‘n’ numbers between ‘x’ and ‘y’ then multiply the numerator and denominator by (n+1).

Hence, According to the given question we need to find 5 numbers between 3/5 and 4/5. so multiply by ‘5+1=6’ in numerator and denominator.

\frac{3}{5}=\frac{3\times6}{5\times6}=\frac{18}{30}and\frac{4}{5}=\frac{4\times6}{5\times6}=\frac{24}{30}

five rational numbers between 3/5 and 4/5 are:

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

4. State whether the following statements are true or false. Also, 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.