RRB NTPC Graduate – Study plan

What is the Number System?

The number system is the way we classify and work with numbers. It is the foundation of almost every Mathematics question in RRB NTPC.

Types of numbers

• Natural numbers: 1, 2, 3, 4, ...
• Whole numbers: 0, 1, 2, 3, ...
• Integers: ..., -2, -1, 0, 1, 2, ...
• Rational numbers: numbers of the form p/q where q is not 0 (e.g. 3/4, -2, 0.5)
• Irrational numbers: non-terminating, non-repeating decimals (e.g. √2, π)
• Prime numbers: exactly two factors, 1 and itself (2, 3, 5, 7, 11, ...)

Key facts to remember

• 2 is the only even prime number.
• 1 is neither prime nor composite.
• There are 25 prime numbers between 1 and 100.

Quick example

Q. Which of these is a rational number: √3, 0.75, π?

A. 0.75 = 3/4, so 0.75 is rational.

Analogy

Analogy: The number family tree

Think of numbers as one big family tree:

• Natural numbers (1, 2, 3 …) are the children who start counting.
• Add 0 and they become whole numbers — the family now includes the empty chair.
• Add the negative relatives and you get integers.
• Allow sharing (fractions like 3/4) and the family grows into rational numbers.
• Relatives whose decimals never end or repeat (√2, π) are the irrational cousins.
• Everyone together forms the real numbers.

Just as every child belongs to the whole family, every natural number is also a whole number, an integer, a rational number and a real number.