Question

EXERCISE 1.1
1. Is zero a rational number?can you write it in the from p/q,where p and q are integers and q=0?

2. Find six rational numbers between 3 and 4.

3. Find five rational numbers between and
3/5and4/5

4. State whether the following statements are true or false. Give reasons for your answers
(1) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number,​

Answer 1

1) yes, 0 is a rational number as it can written in the form of p by q where the p and q are integers and q is not equal to zero .

2) here n = 6

$so \: \: \: n + 1 = 6 + 1 = 7$

Now ,

$3 = \frac{3 \times 7}{7 \times 1} = \frac{21}{7} \\ \\ \\ 4 = \frac{4 \times 7}{7 \times 1} = \frac{28}{7}$

so,

the six ratio in numbers are :

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

3) in pic

4) I) true

ll ) false

lll) false

Answer 2

Exercise 1.1

1. Zero is a rational number.

$0=\frac{0}{1} \\\\0=\frac{0}{-1}$

∴ '0' can be represented in $\frac{p}{q}$ form.

2. Steps to find rational numbers between two numbers.

Step 1: Make the denominators equal by finding the LCM. Here the denominator is already equal (1) so we don't need to do this step but we have to represent the number in $\frac{p}{q}$ form.

$3=\frac{3}{1} , 4=\frac{4}{1}$

Step 2: Multiply any one number to the denominator and the numerator. You can multiply 10, 100 or any number you like. I will multiply 7 to the numerators and denominators here.

$\frac{3}{1}=\frac{21}{7} ,\ \frac{4}{1}=\frac{28}{7}$

Step 3: List down the numbers.

∴ Rational numbers between 3 and 4 are ⇒

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

3. Steps to find rational numbers between two rational numbers.

Step 1: Make the denominators equal by finding the LCM. Here the denominator is already equal (5) so we don't need to do this step but we have to represent the number in $\frac{p}{q}$ form.

$\frac{3}{5} , \ \frac{4}{5}$

Step 2: Multiply any one number to the denominator and the numerator. You can multiply 10, 100 or any number you like. I will multiply 6 to the numerators and denominators here.

$\frac{3}{5}=\frac{18}{30}$ , $\frac{4}{5}=\frac{24}{30}$

Step 3: List down the numbers.

∴ Rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ are ⇒

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

4.  (i) True - This is true because whole numbers consist of numbers from 0       to infinite.

(ii) False - This is false because integers consist of both negative and positive numbers whereas whole numbers are numbers from 0 to infinite. and they are positive.

(iii) False - This is because whole numbers cannot be represented in $\frac{p}{q}$ form.