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PPT on Number System Class 9th Subject Maths

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ACKNOWLEDGEMENT

We would like to thank Ranveer Singh sir for giving us an opportunity to express ourselves via mathematical projects. We are also thankful to our principal Mr. Nem Singh sir for letting us do such a wonderful project. Also, we thank our friends for their ideas and co-operation they provide to us. We are grateful to all of them.




INTRODUCTION
A number system defines a set of values used to represent a quantity. We talk about the number of people attending school, number of modules taken per student etc.
Quantifying items and values in relations to each other is helpful for us to make sense of our environment.
The study of numbers is not only related to computers. We apply numbers everyday, and knowing how numbers work, will give us an insight of how computers manipulate and store numbers.

Brief Introduction About Numbers
A number is a mathematical object used in counting and measuring. Numerical are often used for labels, for ordering serial numbers, and for codes like ISBNs. In mathematics, the definition of number has been extended over the years to include such numbers as, zero negative numbers, rational number, irrational numbers and complex numbers.

TYPE OF NUMBERS
RATIONAL NUMBERS-A rational number is any number that can be expressed in the form of quotient and fraction P/Q  where Q is not equal to zero.

NATURAL NUMBERS-The counting numbers {1,2,3…} are called natural numbers

Number line-A line on which numbers are marked at intervals, used to illustrate simple numerical operations.

INTEGERS-Positive and negative counting numbers

REAL NMBERS-A real number is a value of a continuous quantity that can represent a distance along a line. 

          Fractions
This is a way of depicting a rational number. Fractions are written as two numbers, the numerator and the denominator, with a dividing bar between them.
In the fraction m/n ‘m’ represents equal parts, where ‘n’ equal parts of that size make up one whole.
If the absolute value of the fraction is greater than 1. Fractions can be greater than, less than, or equal to 1and can also be positive, negative, or zero.

THE DECIMAL NUMBER SYSTEM
The number system we use on day-to-day basis in the decimal system, which is based on ten digits: zero through nine. As the decimal system is based on ten digits, it is said to be base -10 or radix-10 . Outside of specialized requirement such as computing , base-10 numbering system have been adopted almost universally. The decimal system with which we are fated is a place-value system, which means that the value of a particular digit depends both on the itself and on its position within the number.

Decimal Expansion of numbers
           A decimal expansion of a number can be either,
      
        Terminating
        Non-terminating, non recurring

        Non terminating, recurring

Non terminating, recurring
‘‘Recurring’’ means ‘‘repeating’’. In this form, when we divide a number by another, remainder never becomes zero, and also the number does not repeat themselves in any specific pattern. If a number is non terminating and non repeating, they are always classified as irrational number. For example,
0.1010010001000010000010010000……. does have a pattern, but it is not a fixed-length recurring pattern, so the number is irrational.

What is a number line?
A number line is a line  with marks on it that are placed at equal distance apart. One mark on the number line is usually labelled zero and then each successive mark to the left or to the right of the zero represents a particular unit such as 1, or 0.5. it is a picture of straight line.

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