Question

6. Let us write the approximate values of the following fractions, upto 2, 3 &
4 decimal places- (1)(22/3)​

Answer 1

Step-by-step explanation:

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

Ans. Yes, zero is a rational number. We can write it in the form

2. Find six rational numbers between 3 and 4.

Ans. We know that there are an infinite number of rational numbers between two rational numbers.

Therefore, six rational numbers between 3 and 4 can be:

Let x = 3 and y = 4, also n = 6

(x + d), (x + 2d), (x + 3d), (x + 4d), (x + 5d) and (x + 6d).

⇒ The six rational numbers between 3 and 4 are:

3. Find five rational numbers between

⇒ The Five rational numbers between ‘x’ and ‘y’ are:

(x + d); (x + 2d); (x + 3d); (x + 4d)

and (x + 5d).

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.

Ans. (i) True statement

[ ⇒ The collection of all natural numbers and 0 is called whole numbers]

(ii) False statement

[ ⇒ Integers such as –1, –2 are non-whole numbers]

(iii) False statement

[ ⇒ Rational number is not a whole number]

Exercise– 1.2

1. State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.

(ii) Every point on the number line is of the form where m is a natural number.

(iii) Every real number is an irrational number.

Ans. (i) True statement, because all rational numbers and all irrational numbers form the group (collection) of real numbers.

(ii) False statement, because no negative number can be the square root of any natural number.

(iii) False statement, because rational numbers are also a part of real numbers.

2. Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number:

Ans. No, if we take a positive integer, say 4 its square root is 2, which is a rational number.

REMEMBER

According to the Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In the figure:

OB2 = OA2 + AB2

3. Show how can be represented on the number line.

Ans. Let us take the horizontal line XOX’ as the x-axis. Mark O as its origin such that it represents 0.

Cut off OA = 1 unit, AB = 1 unit.

⇒ OB = 2 units

Draw a perpendicular

Cut off BC = 1 unit.