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