Page 15 - Mathematics Class - IX

5. Taking OB as radius and O as a centre, mark the arc on X´OX at M as shown in Fig. (d).
B

2

O A
X' X
M
–2 –1 0 1 2
Fig. (d)
6. OM represents 2 .

OBSERVATION

Since OB = OM, OM = 2 .

INFERENCE

Any irrational number can be represented on a number line.

EXTENDED TASK

1. Represent 3, 5 and 7 on a number line.
2. Prepare a model of dimension 2 using material of your choice.

APPLICATION
This helps in representing irrational numbers such as √2 , √3 , √4 , √5 , √6 , √7 , .... on the number line.

Viva-Voce

1. What are real numbers?
Ans. A set of all rational and irrational numbers is called a real number set and is represented as R.
2. Express 2 in decimals.

Ans. 21 414= . ...
3. Is p a rational number?
22
Ans. No, p is an irrational number. For the convenience in calculation, its value is taken as or 3.14.
4. Which theorem is used in representing irrational numbers on number line? 7
Ans. Pythagoras theorem.
5. Who gave the theorem that ‘Every real number can be represented uniquely on the number line’?
Ans. German Mathematicians Cantor and Dedekind gave this theorem.

6. Do you think 9 is an irrational number?
Ans. Basically, 9 = 3 3× = 3
p 3
Which can be written in form as .
q 1
So, 9 is a rational number.

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