Download Classification of Numbers

Classification of Numbers
Any number that is found on the Real Number Line is
Called a Real Number represented by
A real number runs from negative infinity to positive
Infinity
Natural Number
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Natural Numbers are {0,1,2,3,4,5,6, .....}
No decimals
No Negatives
Zero is part of the natural numbers
The Symbol for Natural Numbers is
Integers
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Integers are numbers like {-3,-2,-1,0,1,2,3}
They are both negative and positive
Only Whole numbers
No Decimals
Zero is included
The symbol for integers is
Rational Number
• Numbers that are Fractions or Repeating
decimals
• Like ½, 1/3 ,-2/3 , 4/6 ,-8/9, 0.333...,-0.666.. etc
• Rational comes from Ratio , which means we are
dealing with a numerator and denominator
• The numerator and denominator are both
INTEGERS or
(The denominator is never 0)
• The symbol for Rational Numbers is
Irrational Numbers
• A number with an INFINITE , NON REPEATING
DECIMAL representation is irrational
• E.g
= 3.14159......
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3  1.1732...
2  1.4142...
5  2.236...
• Are irrational numbers represented by
The real numbers (Exam Question)
The real numbers (Exam Question)
3.1416
1/5
-1
5
0.863343...
-3
0.4
0.33..
Some questions
• Q: Are all Natural Numbers also Integers?
• Ans: Yes the set of Natural Numbers is contained
in the set of integers
• Q: Are all Integers also Natural Numbers?
• Ans: No ! For example -2 , -1 ...etc are not Natural
Numbers, but they are integers
• Q: Are all Integers also Rational Numbers?
• Ans: Yes the set of Integers is Contained in the set
of Rational Numbers
Some questions
• Q: Are all irrational numbers also Real
Numbers?
• Ans: Yes, every number that exists on the real
number line is a real number!
• Natural Numbers, Integers, Rational and
Irrational Numbers are all Real Numbers.