# Mathematics Summary Unit-1 Number System: Objectives and Expected Background Knowledge

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• In Mathematics, Number Systems, various notational systems that have been or are being used to represent the abstract quantities called numbers. A number system is defined by the base it uses, the base being the number of different symbols required by the system to represent any of the infinite series of number.

• From time immemorial human beings have been trying to have a count of their belongings – goods, ornaments, jewels, animals, trees, sheeps/goats, etc. by using various techniques.

• Putting scratches on the ground/stones

• By storing stones – one for each commodity kept/taken out.

• This was the way of having a count of their belonging without having any knowledge of counting.

The invention of number system including zero and the rules for combining them helped people to reply questions of the type:

• How many apples are there in the basket?

• How many speakers have been invited for addressing the meeting?

• What is the number of toys on the table?

• How many bags of wheat have been the yields from the field?

The answers to all these situations and many more involve the knowledge of numbers and operations on them.

## Objectives

After studying this lesson, you will be able to

• Illustrate the extension of system of numbers from natural numbers to real (rational and irrational) numbers

• Identify different types of numbers

• Express an integer as a rational number

• Express a rational number as a terminating or non-terminating repeating decimal, and vice-versa

• Find rational numbers between any two rationales

• Represent a rational number on the number line

• Cites examples of irrational numbers

• Represent on the number line

• Find irrational numbers between any two given numbers

• Round off rational and irrational numbers to a given number of decimal places

• Perform the four fundamental operations of addition, subtraction, multiplication and division on real numbers.

In this lesson, we will present a brief review of natural numbers, whole numbers and integers. We shall then introduce about rational and irrational numbers in detail. We shall end the lesson after discussing about real numbers.