Points A and B are marked on the number line; the small marks are 0.1 apart. Which of these numbers lies between A and B?

Class 9Number SystemsNumber Systems

Step-by-Step Solution

A is 1.3 and B is 1.5. Since

1. 3^{2} = 1.69 < 2 < 2.25 = 1. 5^{2}, 2 \approx 1.414

lies between them.

3 \approx 1.73

and

5 - 1 \approx 1.24

do not, and 1.29 is just left of A.

Answer: D) √2

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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