Class 9 Maths Number Systems Number System

Number system is system of Numeration. It is a writing system for expressing number. Typically used to count numbers, measure temperature, find area of an object, and numerically represent any data.

The classification is based on History of numbers.

Natural Numbers: Natural numbers were the first to come. They are denoted by N. These numbers can be counted on fingers. E.g.: 1, 2, 3, 4, 5, 6, 10, 15, 20, 21 etc

Whole Number: Aryabahatta, famous Mathematician gave ‘0’ to the number system. It is very powerful number. Anything multiplied by 0 becomes 0. This new number 0, when added to the Natural numbers gave a new set of numbers called Whole number. E.g.: 0, 2, 3 5 etc. It is denoted by W. It has all natural numbers plus 0. Note that Whole number has only positive numbers. All Natural numbers are whole number but the reverse is not true.

Integers: Field of Mathematics advanced & there was a need for Negative numbers as well. If we add negative numbers to the whole number, we get Integers. It is denoted by “Z”. Z came from word Zahlen that means “to count”. It is used to express temperature, latitude, longitude etc which can have negative values. E.g.: -20oC. All Whole numbers are Integers, but the reverse is not true. Refer the image below for clarity.

Rational Numbers:  Field of Mathematics advance further & concept of division came into picture. Numbers that can be represented in the form of p/q where P& Q are Integers & q≠ 0 were called Rational Number. Word Rational number came from Ratio. It is demoted by Q. Q letter is taken from word Quotient. E.g.: ½, 9/5 etc. There is Infinite Rational Numbers between any 2 Rational Numbers. All Integers are Rational Number , but the reverse is not true.

Irrational Numbers:  Field of Mathematics advance further & mathematicians found that there are some numbers that can’t be written in the form of p/q where p& q are integers & q≠0. They call it irrational Numbers. Eg √2, √3

Real number: Both Rational & Irrational Numbers together forms Ream number. It is denoted by R. Evert point on the number line is a Real number. E.g.: √2, -7, 4/9 , 0, 5 etc. All rational numbers are real number. All irrational numbers are real number, but the reverse is not true.

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