# Representation of Real Numbers on number line

For representation of real numbers on number line, use the following steps :Represent √x on 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 D

**Step 6**Taking B as the centre and BD as radius draw an arc cutting OC produced at E.

Point E so obtained represents √x.

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**Examples on representation of real numbers on number line :**

**1) 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 D

**Step 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).

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**2) 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

**Real-Numbers**

• Real Numbers

• Representation of real numbers on number line

• Operations on Real Numbers

• Rationalization of denominator

• Real Numbers

• Representation of real numbers on number line

• Operations on Real Numbers

• Rationalization of denominator

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