1. Numbers
Types of numbers :
Real Numbers
Any number which contains a real value i.e. it can be expressed on a number line is called real number. For example 1/2, 5 , 5.677,√2 etc-
Imaginary Numbers
These numbers do no have a real value, and they cannot exist on a number line. For example √-1,√-5 etc
Real Numbers can be further classified into :
Natural Numbers (N)
These are numbers that can exist in nature, and can be counted with such as 1,2,3,4,...Whole Numbers
Whole numbers are the collection of all natural numbers as well as zero. So whole nos are 0,1,2,3,4,...
- 0 is the only whole number which is not a natural number
Integers (Z)
These are the collection of zero, natural numbers, and their negative values.- Z = {... -3, -2, -1, 0, 1, 2, 3, ... }
- 0 is neither a positive integer nor a negative integer.
Rational Numbers (Q)
The numbers which can be represented in the form p/q , where p and q are integers and q is not equal to 0.
- = {... -2, -1, -0.5, -0.33, 0, 0.46, 0.55, 1, ... }
- All integers are also Rational Numbers
Irrational Numbers
These numbers cannot be expressed in the form of p/q, such that both p and q are integers, and q is not equal to zero.
- = {... -√3, -√2, √2, √3, √4 ...} (Note that -√2 is different from √-2)
- When expressed in decimal form, these have non-terminating, non-repeating expansions. For example √2 = 1.41421356237309... (this is only an approximate value)
Natural Numbers are often classified into :
Even Numbers: A number is said to be even if it is perfectly divisible by 2. For example : 2, 4, 6, 8, 10 etc
Odd Numbers: A number is said to be odd if it is not perfectly divisible by 2, ie, when you get a remainder when dividing it by 2. For example: 1, 3, 5, 7 etc
Prime Numbers: A number is said to be prime if it is perfectly divisible only by 1 and itself. For example : 2, 3, 5, 7, 11 etc
2 is the only even prime number.
Composite Numbers: A number is said to be composite if it is perfectly divisible by atleast one number other than 1 and itself. For example: 4, 6, 8, 9, 12, 15 etc
One is neither a prime number nor a composite number.
No comments:
Post a Comment