UNDERSTANDING CONCEPT OF INTEGERS

To under stand the concept of integers, first you have to understand the following concepts:

Concept of NUMBER LINE:

In order to understand the concept of integers, first of all we have to understand concept of NUMBER LINE. A number line may be depicted as inder:

6____5____4____3__2___1__0___-1___-2___-3____-4____-5____-6

              +ve_____________Number line____________-ve

            --Value always positive --                                                              -- Value always negative--

                 (Greater than Zero)                                                                            (Less than Zero)

In order to understand the use of a Number line we have to understand the place values of positive and negative integers in term of a Number line. For your convenience of understanding, you presume that you are standing on the surface of a earth, Your feet are placed at Zero value (Earth). Then the distance from your feet beyond head towards sky, as it goes increasing up above your head is positive side of a number line and the distance from your feet towards earth’s center as it goes increasing is negative. Instead of representing a number line upside down, we have put it horizontally. Now the left side of number line from Zero is is positive and right side from zero is negative. By this hypothesis, on positive side +6 is greater than +1 but on negative side -6 is less than -1.

For adding and subtracting purposes we represent numbers according to the above principal as under:

Placement of Positive integer before decimel	Place value
First +ve integer to be placed below Ones	1
Second +ve integer to be placed below Tens	10
Third +ve integer to be placed below Hundred	100
Fourth +ve integer to be placed below Thousands	1000
Fifth +ve integer to be placed below Ten Thousands	10000
Sixth +ve integer to be placed below Lakh	100000
Seventh +ve integer to be placed below	1000000
etc…..	etc…

Placement of Negative integers after decimal	Place value
First -ve integer to be placed below One/ Ten	1/10
Second -ve integer to be placed below  One/Hundred	1/100
Third -ve integer to be placed below One/Thousand	1/1000
Fourth -ve integer to be placed below One/Ten Thousand	1/10000
Fifth -ve integer to be placed below  One/Lakh	1/100000
Sixth -ve integer to be placed below One/ Ten Lakh	1/1000000
Seventh -ve integer to be placed below One/ Crore	1/10000000
etc…..	etc…

Exact value can be determined by multiplying the Number concerned by above place value

Consider:      Digits     2675.2134 and 1634.1023 and 200. 3

Thousands	Hundreds	Tens	Ones	Decimel	1/10	1/100	1/1000	1/10000
2	6	7	5	.	2	1	3	4
1	6	3	4	.	1	0	2	3
0	2	0	0	.	3	0	0	0

For our convenience sake we may put zeros in empty spaces on either side while adding or subtracting. This will not make any difference but will be convenient.

While adding when total exceeds 9 one carry forward digit will be added to next place value digit and so on.

                                                                                   ……to be continued