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Question

Represent 9.3 on the number line.

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Solution

Step 1: Draw a line segment of unit 9.3. Extend it to C such that BC is 1 unit.

Step 2: Now, AC = 10.3 units. Find the centre of AC and name it as O.

Step 3: Draw a semi-circle with radius OC and centre O.

Step 4: Draw a perpendicular line BD to AC at point B which intersects the semicircle at D. Also, Join OD.

Step 5: Now, OBD is a right-angled triangle.

Here, OD=10.32 (radius of semi-circle), OC=10.32, BC = 1

OB = OC – BC = (10.32) – 1 = 8.32

Using Pythagoras theorem,

OD2=BD2+OB2

(10.32)2=BD2+(8.32)2BD2=(10.32)2(8.32)2BD2=(10.328.32)(10.32+8.32)BD2=9.3BD=9.3

Thus, the length of BD is 9.3.

Step 6: Taking BD as radius and B as centre draw an arc which touches the line segment. The point where it touches the line segment is at a distance of 9.3 from B as shown in the figure.


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