(I) Any rational number corresponds to a point on the number line, but an irrational number cannot be represented by a point on the number line.

(II) Both rational and irrational numbers can be represented by points on the number line.

(III) Whether it is a rational or irrational number, we cannot represent it as a point on the number line.

Step: 1

From the above statements, "Both rational and irrational numbers can be represented by points on the number line" is the correct statement.

Correct Answer is : II only

Step: 1

[1 6 = 4.]

Step: 2

Approximate value of 3 = 1.732

Step: 3

So, 4 8 = 4(1.732) = 6.928

Step: 4

Mark the number on the number line.

Step: 5

So, Figure 1 represents the approximate location of 4 8 .

Correct Answer is : Figure 1

Step: 1

Step: 2

= 32

[9 = 3]

Step: 3

Approximate value of 2 = 1.414

Step: 4

Step: 5

The point P approximately represents 4.242.

Step: 6

So, the point P represents 1 8 on the number line.

Correct Answer is : P

Step: 1

Step: 2

= 22

[4 = 2]

Step: 3

Approximate value of 2 = 1.414

Step: 4

Step: 5

The point J approximately represents 2.828.

Step: 6

So, the point J represents 8 on the number line.

Correct Answer is : J

Step: 1

3 lies between the perfect squares 1 and 4.

Step: 2

Step: 3

Step: 4

Step: 5

So, the point P represents 3 on the number line.

Correct Answer is : P

Step: 1

The point on the line lies between 0 and 5.

Step: 2

Among the choices 1 7 , 2 lie between 0 and 5.

Step: 3

The point on the number line is closer to 5.

Step: 4

Among the choices the approximate value of 1 7 is closer to 5.

Step: 5

So, the point on the number line represents 1 7 .

Correct Answer is : 1 7

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