# REAL NUMBER SYSTEM

Real number system :

In the development of science, we should know about the properties and operations on numbers which are very important in our daily life.

In the earlier classes we have studied about the whole numbers and the fundamental operations on them.

Now, we extend our study to the integers, rationals, decimals, fractions and powers in this section.

The picture given below clearly illustrates the real number system.

## Numbers

In real life, we use Hindu Arabic numerals - a system which consists of the symbols 0 to 9.

This system of reading and writing numerals is called, “Base ten system” or “Decimal number system”.

## Natural numbers

Counting numbers are called natural numbers. These numbers start with smallest number 1 and go on without end. The set of all natural numbers is denoted by the symbol ‘N’.

N  =  { 1, 2, 3, 4, 5, .......} is the set of all natural numbers.

## Whole numbers

Natural numbers together with zero (0) are called whole numbers. These numbers start with smallest number 0 and go on without end.

The set of all whole numbers is denoted by the symbol ‘W’.

W  =  { 0, 1, 2, 3, 4, 5, .......} is the set of all whole numbers.

## Integers

The whole numbers and negative numbers together are called integers.

The set of all integers is denoted by Z.

Z  =  {... - 2, - 1,0,1,2, ...,} is the set of all integers

## Fractions

A fraction is a part or parts of a whole.

In a fraction, the number above the line is called the numerator and the number below the line is called the denominator.

## Decimal numbers

A number in which we have "point" is called as decimal number.

A decimal number has two parts namely an integral part and a decimal part.

Examples :

1)  Let us consider the decimal number 0.6

0.6 can be written as 0 + 0.6

Here, integral part  =  0 and decimal part  =  6

2)  Let us consider the decimal number 7.2

7.2 can be written as 7 + 0.2

Here, integral part  =  7 and decimal part  =  2

In a decimal number the digits to the left of the decimal point is the integral part.

The digits to the right of the decimal point is the decimal part.

The value of all the decimal parts is less than 1.

## Rational numbers

So, any number in the form of fraction can be treated as rational number.

Examples of rational number :

5,   2.3,   0.02,   5/6

Because all these numbers can be written as fractions.

5 = 5/1

2.3 = 23/10

0.02 = 2/100 = 1/50

5/6 (This is already a fraction)

Apart from the above examples, sometimes we will have recurring decimals like 1.262626..........

1.262626........ is a non terminating recurring decimal.

All these recurring decimals can be converted into fractions and they are also rational numbers.

Important note :

All the fractions and decimal numbers will come under this category.

Hence, all the fractions and decimal numbers to be considered as rational numbers.

## Irrational numbers

A number which can not be converted into fraction is called as irrational numbers.

Examples of irrational number :

All the above non terminating numbers can not be converted into fractions.

Because, they do not have repeated patterns.

When we are trying to find square of a number which is not a perfect square, we get this non repeating non terminating decimal.

And these non recurring decimals can never be converted in to fractions and they are called as irrational numbers.

Already we know the stuff  that recurring decimal can be converted into fraction and it is rational.

After having gone through the stuff given above, we hope that the students would have understood "Real number system".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6