# 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.

## Expected Background Knowledge

Basic knowledge about counting numbers and their use in day-to-day life.