About "Decimals"

Decimals :

We have learnt about very big numbers (a number with more number of digits) and fractions which is less than 1. We often use fractions like 1/4, 1/2, 3/4.

By addition or subtraction of fractions, we got fractions like 3/8, 5/8, 7/16.

Very numbers also can be written as fractions. Why can't we use fractions to represent all small numbers ?

It is because of the difficulties in using fractions. 

(2/3) + (3/4)  =  ?

We have to convert them into like fractions by finding equivalent fractions and then add.

It is easy, if all the fractions are in the form of 1/10, 1/100, 1/1000...

(15/100) + (235/1000) can be easily added as

(150/1000) + (235/1000)  =  385/1000

It was easy to use multiples of 10 in measurements. It will be easy if small numbers can be written as fractions with multiples of ten as denominators.  

One tenths (1/10)

Look at the figure given below. 

David has 6 candy bars, each connected with 10 connected pieces. 

He gave some pieces to his friends and he finds that 

1 piece out of 10 from the first bar

5 pieces out of 10 from the second bar

2 piece out of 10 from the third bar

3 pieces out of 10 from the fourth bar

6 piece out of 10 from the fifth bar

8 pieces out of 10 from the sixth bar

We can write them as 

1/10, 5/10, 2/10, 3/10, 6/10, 8/10 in fractions. 

This can be written as 0.1, 0.5, 0.2, 0.3, 0.6, 0.8 in dec. numbers. 

0.1 is read as zero point one. The point between between the numbers is called decimal point

Sometimes decimal is also known as "dec."

Dec. numbers - definition

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

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

Examples :

1)  Let us consider the dec. number 0.6

0.6 can be written as 0 + 0.6 

Here, integral part  =  0 and dec. part  =  6

2)  Let us consider the dec. number 7.2

7.2 can be written as 7 + 0.2 

Here, integral part  =  7 and dec. part  =  2

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

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

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

Decimal place value

Dec. place value is nothing but the one which explains the position of each digit which comes after the dec. point.

Dec. place value chart

To have better understanding of the above chart, let us look at an example.

Dec. place value - Example

After having gone through the stuff given above, we hope that the students would have understood "Dec. numbers". 

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