NCERT Class 9 Solutions: Number Systems (Chapter 1) Exercise 1.5 – Part 2

Q-4 Represent 9.3 on the number line.

Solution:

  • Step 1: Draw a line segment of unit 9.3. Extend it to C so that BC is of 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=OCBC=(10.32)1=8.32 Using Pythagoras theorem, OD2=BD2+OB2 (10.32)2=BD2+(8.32)2 BD2=(10.32)2(8.32)2 BD2=(10.328.32)(10.32+8.32) BD2=9.3 BD2=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 O as shown in the figure.

Draw a line segment of units 9.3 on the number lines

Draw a Line Segment of Units 9.3

Draw a line segment of units 9.3 on the number lines

Q-5 Rationalise the denominators of the following

  1. 17

  2. 176

  3. 15+2

  4. 172

Solution:

  1. 17

    =1×77×7

    =77

  2. 176

    =1(7+6)(76)(7+6)

    =7+6(7)2(6)2

    =7+676

    =7+61

    =7+6

  3. 15+2

    =1(52)(5+2)(52)

    =52(5)2(2)2

    =5252

    =523

  4. 172

    =1(7+2)(72)(7+2)

    =7+2(7)2(2)2

    =7+274

    =7+23

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