A student says: “ $\frac{9}{3}$ is written as a fraction, so it cannot be an integer.” What is wrong with this?

Class 9Number SystemsNumber Systems

Step-by-Step Solution

The way a number is written does not decide which family it belongs to — its value does.

\frac{9}{3} = 3

, an integer (and therefore also whole, natural and rational).

Answer: C)

\frac{9}{3} = 3

, so it is an integer as well as a rational number

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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