The number 0.101001000100001… (with an increasing number of zeros) is:

Class 9Number SystemsNumber Systems

Step-by-Step Solution

The pattern of zeros keeps increasing, so the decimal never terminates and never repeats a fixed block. Non-terminating non-recurring → irrational.

Answer: A) Irrational

Every real number has a unique location on the number line.

- Rationals: easy to plot.

\frac{3}{4}

→ 3 quarters past 0.
- Irrationals like

2

can be plotted geometrically: a right triangle with legs 1 and 1 has hypotenuse

2

(Pythagoras). Use a compass to mark off

2

on the number line from 0.

You can extend this —

3

from a triangle with legs

2

and 1,

4 = 2, 5

from legs 2 and 1, etc. (the spiral of Theodorus).

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