The document Representation of Real Numbers on number line & Operations on real numbers Notes | EduRev is a part of the Class 9 Course Mathematics (Maths) Class 9.

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For the representation of real numbers on the number line, use the following steps:

Represent √x on the number line.

Step 1:Draw a line and mark a point A on it.Step 2:Mark a point B on the line drawn such that AB = x cm.Step 3:Mark a point C on AB produced such that BC = 1 cm.Step 4:Find mid-point of AC (x+1). Let the mid-point be O.Step 5:Taking O as centre and OC = OA [(x+1)/2] as radius draw a semi-circle. Also draw a line passing through B perpendicular to OB. Let it cut the semi-circle at DStep 6:Taking B as the centre and BD as radius draw an arc cutting OC produced at E.Point E so obtained represents √x.

**Examples: **

**Represent √(9.3) on the number line. **

Step 1:Draw a line and mark a point A on it.Step 2:Mark a point B on the line drawn such that AB = 9.3cm.Step 3:Mark a point C on AB produced such that BC = 1 cm.Step 4:Find mid-point of AC (9.3+1). Let the mid-point be O.Step 5:Taking O as center and OC = OA [10.3/2] as radius draw a semi-circle. Also draw a line passing through B perpendicular to OB. Let it cut the semi-circle at DStep 6:Taking B as the center and BD as radius draw an arc cutting OC produced at E.Point E so obtained represents √(9.3).

**Visualize 3.765 on the number line using successive magnification. **

Step 1:Since the given number lies between 3 and 4, look at the portion of the number line between 3 and 4.Step 2:Divide the portion between 3 and 4 into 10 equal parts and mark each point of the division as shown in Fig. 1.Step 3:The 7th mark and 8th mark of this sub-division corresponds to 3.7 and 3.8 respectively and 3.765 lies between them (3.7 < 3.765 < 3.8)Step 4:Again divide the portion between 3.7 and 3.8 into 10 equal parts. Now 3.765 lies between its 6th and 7th mark (3.76 < 3.765 < 3.77).Step 5:Divide the portion between 3.76 and 3.77 again into ten equal parts. Therefore, the 5th mark of this sub-division mark represents 3.765 as shown in fig.3

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