Types of Number

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Different Types of Numbers

Our number system is called the Hindu-Arabic system because it was developed by Hindus and spread by Arab traders. It uses place value based on powers of ten, and any number can be written using the digits 0 to 9.

Here are the main types of numbers you need to know:

Natural Numbers
These are the counting numbers you use every day: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on. They go on forever. Natural numbers don't include zero or negative numbers—just the positive whole numbers you count with.

Integers
Integers include all whole numbers—both positive and negative—plus zero. Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...

• Positive integers: 1, 2, 3, 4, 5, ... (these are the same as natural numbers)
• Zero: 0 (this is neither positive nor negative)
• Negative integers: -1, -2, -3, -4, -5, ...

Prime Numbers
A prime number has exactly two factors: itself and 1. This means it can only be divided evenly by 1 and itself.

The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...

Important notes:

• 1 is NOT a prime number (it only has one factor, not two)
• 2 is the only even prime number
• All other prime numbers are odd

Square Numbers
A square number is made when you multiply a whole number by itself.

Examples:

• 1 × 1 = 1 (so 1 is a square number)
• 2 × 2 = 4 (so 4 is a square number)
• 3 × 3 = 9 (so 9 is a square number)
• 4 × 4 = 16 (so 16 is a square number)
• 5 × 5 = 25 (so 25 is a square number)

Cube Numbers
A cube number is made when you multiply a whole number by itself, and then by itself again.

Examples:

• 1 × 1 × 1 = 1 (so 1 is a cube number)
• 2 × 2 × 2 = 8 (so 8 is a cube number)
• 3 × 3 × 3 = 27 (so 27 is a cube number)
• 4 × 4 × 4 = 64 (so 64 is a cube number)
• 5 × 5 × 5 = 125 (so 125 is a cube number)

Rational Numbers
A rational number is any number that can be written as a fraction (one whole number divided by another whole number). The word "rational" comes from "ratio."

Examples:

• 1/2 (one half)
• 3/4 (three quarters)
• 5 (this equals 5/1, so it's rational)
• 0.25 (this equals 1/4, so it's rational)
• -2/3 (negative fractions are also rational)

All integers are rational because they can be written as fractions (like 7 = 7/1).

Irrational Numbers
An irrational number cannot be written as a fraction. When written as a decimal, it goes on forever without repeating.

Examples:

• π (pi) = 3.14159... (goes on forever)
• √2 (square root of 2) = 1.41421... (goes on forever)
• √3 (square root of 3) = 1.73205... (goes on forever)

Reciprocals
The reciprocal of a number is 1 divided by that number. You can also think of it as "flipping" a fraction upside down.

Examples:

• The reciprocal of 5 is 1/5
• The reciprocal of 2/3 is 3/2
• The reciprocal of 1/4 is 4
• The reciprocal of 10 is 1/10

Important: Zero has no reciprocal because you cannot divide by zero.