Chapter 1 · Mathematics

Natural, Whole, Integers and Rational Numbers

Each new family of numbers answers a question the old one could not, and every family lives inside the next: N ⊂ W ⊂ Z ⊂ Q.

Key points

Family	Set	The question it answers
Natural numbers (N)	{1, 2, 3, 4, …}	How do we count?
Whole numbers (W)	{0, 1, 2, 3, …}	How many apples on an empty plate? Zero.
Integers (Z)	{…, −3, −2, −1, 0, 1, 2, 3, …}	Temperature below zero, like −5 °C?
Rational numbers (Q)	p/q, p and q integers, q ≠ 0	Half a pizza each for two friends? 1/2.

An integer n is rational because n = n/1 (5 = 5/1, −3 = −3/1).
Rationals can be positive, negative or zero: 3/4, −7/2, 0 = 0/5.
A rational number has many forms: 1/2 = 2/4 = 50/100.
Not every number is rational: √2 and π cannot be written as p/q (irrational, the next topic).

Rational number = p/q, with p, q integers and q ≠ 0

7 is natural, whole, an integer and rational.
0 is whole, an integer and rational, but not natural (in CBSE / NCERT, N starts at 1).
−4 is an integer and rational, but not whole or natural.
2/3 and −1/2 are rational only.

5 questions. Choose an answer for each, then submit to see your score and the explanations.