On a number line, where does the point for $20$ lie?

Class 9Number SystemsNumber Systems

Step-by-Step Solution

4^{2} = 16

and

4. 5^{2} = 20.25

. Since 16 < 20 < 20.25, the number

20

≈ 4.47 lies between 4 and 4.5 — just short of 4.5.

Answer: A) Between 4 and 4.5

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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