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

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**Q-4** Represent 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, 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, (radius of semi-circle, Using Pythagoras theorem,⇒ ⇒ ⇒⇒ ⇒ Thus, the length of BD is .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 from O as shown in the figure.

**Q-5** Rationalise the denominators of the following

Solution: