Integer is a whole number which is not a fraction, that is it can be either positive, negative or zero. Thus the numbers -20, -10, 0, 10, 50, 98, 540 are integers. It can not have decimals. It is commonly used in computer programming as a data type. It can also be used to find out item's location in an array. If two integers are added, subtracted or multiplied, then the output is also an integer. Where as if one integer is divided with other integer, then the result may be an integer or a fraction.
When we think of the number, we first of all think of natural numbers: 1, 2, 3, 4, 5, ...... which are also called positive integers. By applying the operation of subtraction, we get the number zero and negative integers. The set {.....-4, -3, -2, -1, 0, 1, 2, 3, 4,........} is called the set of integers. By division operation, we get the positive and negative fractions. The integers and fractions together constitute the class of rational number p/q, where p and q are integers but q is not equal to 0.
Integers and long integers:
Numbers which includes positive integers{ 1, 2, 3, 4, .....} and negative integers{-1, -2, -3, -4,......} with zero{0} are called integers. There is no fractions or decimal points are included in the integers. They are represented by Z.
Therefore,
Z={ … -4, – 3, – 2, – 1, 0, + 1, + 2, + 3, +4 ….}
+ 1, + 2, + 3, … are positive integers.
– 1, – 2, – 3, … are negative integers.
Note:
Positive numbers can be written even without the ‘+’ sign.
For example, +5, +4, +3, +2, +1 are written as 5, 4, 3, 2, 1.
Thus, Z = {…… – 3, – 2, – 1, 0, 1, 2, 3, ……}
The integers are represented on the number line as follows:
On the number line, the numbers which are to the right of zero are called positive integers. The numbers which are to the left of zero are called negative integers.
(1) Every natural number or a whole number.
(2) Every whole number is an integer.
Order in long integer:
When we think of the number, we first of all think of natural numbers: 1, 2, 3, 4, 5, ...... which are also called positive integers. By applying the operation of subtraction, we get the number zero and negative integers. The set {.....-4, -3, -2, -1, 0, 1, 2, 3, 4,........} is called the set of integers. By division operation, we get the positive and negative fractions. The integers and fractions together constitute the class of rational number p/q, where p and q are integers but q is not equal to 0.
Integers and long integers:
Numbers which includes positive integers{ 1, 2, 3, 4, .....} and negative integers{-1, -2, -3, -4,......} with zero{0} are called integers. There is no fractions or decimal points are included in the integers. They are represented by Z.
Therefore,
Z={ … -4, – 3, – 2, – 1, 0, + 1, + 2, + 3, +4 ….}
+ 1, + 2, + 3, … are positive integers.
– 1, – 2, – 3, … are negative integers.
Note:
Positive numbers can be written even without the ‘+’ sign.
For example, +5, +4, +3, +2, +1 are written as 5, 4, 3, 2, 1.
Thus, Z = {…… – 3, – 2, – 1, 0, 1, 2, 3, ……}
The integers are represented on the number line as follows:
On the number line, the numbers which are to the right of zero are called positive integers. The numbers which are to the left of zero are called negative integers.
(1) Every natural number or a whole number.
(2) Every whole number is an integer.
Order in long integer:
- On the number line, we find that the number value increases as we move to the right and decreases as we move to the left.
- If we represent two integers on the number line, the integer on the right is greater than the integer on the left.
- In other words, the integer on the left is lesser than the integer on the right.
For example, consider the following points marked on the number line in the figure given below:
In the above figure,
4 is to the right of 2 `:.` 4 > 2
2 is to the right of -1 `:.` 2 > -1
-5 is to the left of -1 `:.` -5 < -1
Example problems:
Example 1: Which is smaller? -2 and -5
Solution:
First, mark the integers -2 and -5 on the number line.
On the number line, -5 is on the left side of -2.
Therefore, -5 is smaller than -2
That is -5 < -2.
Example 2: Write the following integers in ascending order.
3,-2,0,-4,-1,5
Solution:
First mark these integers on the number line.
Now arrange the integers from left to right to get them in ascending order
-4 < -2 < -1 < 0 < 3 < 5
Therefore, the ascending order is -4, -2, -1, 0, 3, 5.
In the above figure,
4 is to the right of 2 `:.` 4 > 2
2 is to the right of -1 `:.` 2 > -1
-5 is to the left of -1 `:.` -5 < -1
Example problems:
Example 1: Which is smaller? -2 and -5
Solution:
First, mark the integers -2 and -5 on the number line.
On the number line, -5 is on the left side of -2.
Therefore, -5 is smaller than -2
That is -5 < -2.
Example 2: Write the following integers in ascending order.
3,-2,0,-4,-1,5
Solution:
First mark these integers on the number line.
Now arrange the integers from left to right to get them in ascending order
-4 < -2 < -1 < 0 < 3 < 5
Therefore, the ascending order is -4, -2, -1, 0, 3, 5.
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