Types of Number

Natural numbers: These are the set of positive integers starting from 1 (1,2,3,4,5…). They are often used in counting and ordering.
Whole numbers: This set consists of all natural numbers including 0 (0,1,2,3,4,5…).
Integers: These are all the whole numbers and their opposites (-3,-2,-1,0,1,2,3…). They are used for operations like subtraction and measures below zero.
Rational numbers: These are all numbers that can be expressed as a fraction, where both the numerator and denominator are integers. The denominator cannot be zero. All integers are rational numbers (for instance 5 can be written as 5/1). Decimal representations of rational numbers are either terminating or recurring.
Irrational numbers: These numbers cannot be expressed as a ratio or fraction. They are non-repeating and non-terminating. An example of an irrational number is the square root of 2 or Pi.
Real numbers: This set includes all the rational and irrational numbers. Basically, all numbers that can be found on the number line are real numbers.
Prime numbers: These are natural numbers greater than 1, which have no positive integer divisors other than 1 and itself. Examples are 2, 3, 5, 7, 11, 13, 17 etc.
Composite numbers: These are natural numbers that have at least one positive integer divisor other than 1 and itself. All natural numbers greater than 1 that are not prime are composite. Examples are 4, 6, 8, 9, 10 etc.
Even numbers: These are integers that are exactly divisible by 2. Examples include -4, -2, 0, 2, 4, 6…
Odd numbers: These are integers that are not divisible by 2. Examples are -3, -1, 1, 3, 5, 7…
Powers/Indices/Exponents: These are simple multiplication expressions used symbolically to denote multiplication iterated (repeated), where a number is multiplied by itself a number of times. Examples are 2^3, 10^4, 7^0 etc.

Understanding these different types of numbers allows for a more comprehensive grasp of what numbers mean, and how they interact and relate to each other. Knowing how to categorise numbers is an important foundation in mathematic learning.