Are Rational Numbers Whole Numbers

Types of Numbers

Numbers play a vital role in our lives, such every bit counting things, time, money, age and much more. The ten mathematical digits (0 to 9) are used to represent all of these quantities. In this article, we will be discussing the different types of numbers in mathematics with examples.

Dissimilar Types of Numbers

Following are the main types of numbers used in school mathematics.

Natural Numbers

Numbers start from ane and up. NO Null, 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 of the alphabet 'N'.

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

Whole Numbers

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

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

The set up of whole numbers is denoted by W.

W = {0, 1, 2, 3, 4, five, ….}
Examples: 45, 0, 59, eleven, 110 etc.

Integers

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

Z = {-4, -3, -ii, -1, 0, one, 2, three, 4}

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

Rational Numbers

Whatsoever number written in the form of fraction or ratio, i.e., a/b, where a and b are integers.[Tip to think: root word of rational is 'ratio'].

The letter 'Q' denotes a rational number.

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

Examples: 1/4, 2/5, 7/2, ⁻iv/three, 0/1 etc.

Irrational Numbers

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

The letter of the alphabet ' P denotes an irrational number.'
Examples: 𝜋=3.14159…, √3=1.73205, Euler'due south 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 of the alphabet 'R.'

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

>> Prime and Composite Numbers

Attempt IT NOW!

Classify each number in every bit many categories as possible.

(1) -25

(2) 0

(three) one/5

(four) 1

(5) √ii

(6) -16/4

(vii) three.1428571428571….

Reply

1 . Integer, rational, existent
2 . Whole, Integer, rational, and real
three . Rational, real
4 . Natural, whole, Integer, rational, real
5 . Irrational, existent
6 . Integer, rational, real (because -16/4 can exist rewritten as -4)
7 . Irrational, real