# Types of Numbers

### Different Types of Numbers

### Natural Numbers

Numbers start from 1 and up. NO Zero, NO numbers with decimals, and NO Negative numbers are in this group.

Natural numbers are also called** counting numbers or positive integers** because these numbers are used for counting and ordering.

The set of natural numbers is denoted by the letter ‘N’.

N = {1, 2, 3, 4, 5, ….}**Examples: 45, 109, 59, 12, etc.**

### Whole Numbers

Whole Numbers are simply the natural numbers, including zero (i.e., natural numbers + 0).

NO numbers with decimals and NO Negative numbers are in this group.

The set of whole numbers is denoted by W.

W = {0, 1, 2, 3, 4, 5, ….}**Examples: 45, 0, 59, 11, 110 etc.**

### Integers

Integers are all whole numbers and their negatives. The set of integers are denoted by Z.

Z = {-4, -3, -2, -1, 0, 1, 2, 3, 4}

**Examples: -45, 0, 59, -11, 110 etc.**

### Rational Numbers

Any number written in the form of fraction or ratio, i.e., a/b, where a and b are integers. *[Tip to remember: root word of rational is ‘ratio’]*.

The letter ‘Q’ denotes a rational number.

[*Note*: The denominator cannot be 0, but the numerator can be].

**Examples: 1/4, 2/5, 7/2, ⁻4/3, 0/1 etc.**

### Irrational Numbers

A number that **cannot** be written in the form of a fraction or ratio. Irrational Numbers may be endless (never terminating) non-repeating decimals.

The letter ‘ P denotes an irrational number.’**Examples: 𝜋=3.14159…, √3=1.73205, Euler’s constant, etc.**

### Real Numbers

All the numbers that can be found on a number line. It can be natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

Irrational numbers are real numbers, but not all real numbers are irrational numbers. A real number is denoted by the letter ‘R.’

**Examples: 7, ¾, 0.333, √2, 0, -19, 20, 𝜋 etc.**

### TRY IT NOW!

**Classify each number in as many categories as possible.**

(1) -25

(2) 0

(3) 1/5

(4) 1

(5) √2

(6) -16/4

(7) 3.1428571428571….

**Answer**

1 . Integer, rational, real

2 . Whole, Integer, rational, and real

3 . Rational, real

4 . Natural, whole, Integer, rational, real

5 . Irrational, real

6 . Integer, rational, real (because -16/4 can be rewritten as -4)

7 . Irrational, real