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.: -20^{o}C. 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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