1. Introduction to The Decimals

Decimals
Decimals are an extension of our number system For an example 5.75. Here the dot represents a decimal point. Decimals are fractions whose denominators are 10, 100, 1000 etc. A decimal has two parts, namely, the whole number part and decimal part.

Decimal Places : The number of digits contained in the decimal part of a decimal number is known as the number of decimal places.
For example :
3.75 has two decimal places and 85.325 has three decimal places.

Division of a unit in ten equal parts

If an object is divided into 10 equal parts then its each part is one tenth of the whole. It is written as 

 is also written as 0.1 and is read as 'one tenth' or point one'.ss

Ex.     0.5 is read as 5 tenth. or point five.
It can be written as 2.3 and read as two point three.
Let us take an example, there is two tower each consist two blocks and each block is equal to one unit than tower represents 10 units. So, the number shown here is : 

Representing Decimals on number line
We represented fractions on a number line. Let us now represent decimals too on a number line. Let us represent 0.6 on a number line. We know that 0.6 is more than zero but less than one. There are 6 tenths in it. Divide the unit length between 0 and 1 into 10 equal parts and take 6 parts as shown below :

Ex.1     Write the following numbers in the place value table : (a) 20.5    (b) 4.2
Sol.:     Let us make a common place value table, assigning appropriate place value to the digits in the given numbers. We have,

Ex.2     Write each of the following as decimals : (a) Two ones and five-tenths (b) Thirty and one-tenth

Introduction to The Decimals

What is decimal?

 The Numbers used to represent Numbers lower than unit 1 are called decimal numbers. The decimal point or the period plays a significant part in a Decimal Number. This period separates the fractional part and whole number part in a decimal number. Place value of a number can be defined as the value of a number as per the place of that number in a number. Decimals Exemplifications Let us consider a decimal number0.5694 to see the different place values of each number. 

The value of the number at the first place after the decimal point is tenths place value. Tenths can be calculated as 1 unit divided in 10 equal corridor i.e. 0.1. Thus, considering this there are 5 tenths in the number0.5694.
The value of the number at the alternate place after the decimal point is hundredths place value. The number in that place tells you how numerous hundredths are there. Hundredths can be calculated as 1 unit divided in100 equal parts.i.e0.01. thus, considering this there are 6 hundredths in the number0.5694
The value of the number at the third place after the decimal point is thousandths place value. The number in that place tells you how numerous thousandths are present. Thousandths can be calculated as 1 unit divided in1000 equal corridor i.e. 0.001. Thus, considering this there are 9 thousandths in the number0.5694

Ten- thousandths
The value of the number at the fourth place after the decimal point is ten- thousandths place value. The number in that place tells you how numerous ten- thousandths are present. Ten- thousandths can be calculated as 1 unit divided into 10000 equal corridori.e0.0001. Thus, Considering this there are 4 thousandths in the number0.5694

For Example: 

23/10 can be written in decimal as 2.3

23/100 can be written in decimal as 0.23

Knowing about Tenths

As we know that 1 cm = 10 mm, so if we have to find the contrary also
1 mm = 1/10 cm or one-tenth cm or0.1 cm.
Hence, the first number after the numeric represents the tenth part of the whole.

Tenths
This reads as “thirty-four point seven ”.

Representation of decimals on the number line,

 Let us suppose we have to represent0.5 on the number line.
is lesser than 0 and lower than 1 also it can be represented on number line by dividing unit length between 0 and 1 into ten equal corridor and the fifth part will represent 0.5

Knowing about Hundredths,

In Hundredth, one block is divided into 100 equal regions and each part comprises1/100 of the entire block.

If a square is divided into 100 small squares the area of each small square will be1/100 or one hundredth of the entire square.

The area of the lower square shaded red is one hundredth of the entire square.

 The decimal note is1/100 = 0.01.

 Comparing decimals
While comparing two decimal numbers, we consider the following rules
 We compare the place values of integers from left to the right.
Extra zeroes to the right of the last number of a decimal value do not change the value of the number.
Redundant depths between decimal point and a decimal number do not change its value.

Relationship between fractions and decimals

Numbers are values of fragments. Therefore, fragments can be converted into numbers and numbers can be converted into fragments.
Numbers as fragments
Conversion is done by seeing the place value of numbers.
In conversion to bit, the numeric can be written simply as a number with denominator having as numerous depths as the number of integers after the decimal point.

 Problem Write the following as fragments in smallest forms.0.05

 Result

 Then 0 is at Ones place, 0 is at tenths place and 5 is at hundredths place.

= 0 * 1 0 *1/10 5 *1/100

 = 0 05/100

= 5/100

= 1/20

There are two integers after the decimal point.

= 1/20