# Types of Numbers

Research Analyst (Business Research & Consulting)
23 de Feb de 2018
1 de 18

### Types of Numbers

• 1. 1 NUMBER SYSTEM TYPES OF NUMBERS
• 2. Number Systems Lets study about various types of numbers and number line and how to represent these numbers on it….. 2
• 3. Number Systems NUMBERS 0 8 9 Hi… All these are Numerals…. Denoted by Group of digits called Numerals… 3
• 4. Number Systems NATURAL NUMBERS “N” INTEGERS “Z” WHOLE NUMBERS “W” THE NUMBER LINE 4
• 5. Number Systems NATURAL NUMBERS 8 9 Counting numbers are Natural Numbers. 5
• 6. Number Systems ODD NUMBERS Counting numbers not divisible by two “2” EVEN & ODD NUMBERS 6
• 7. Number Systems WHOLE NUMBERS 0 8 9 Counting numbers along with zero are Whole Numbers. 7
• 8. Number Systems INTEGERS 3 4... Counting numbers, zero and negatives of counting are Integers. 8
• 9. Number Systems INTEGERS can be… Negative Integers e.g. -1, -2, -3, -4,… Non Negative Integers e.g. 0, 1, 2, 3, 4,… Positive Integers e.g. 1, 2, 3, 4, 5, 6, 7, 8,… 9
• 10. Number Systems Denoted by ‘r’ are numbers which can be written in p/q form, where p and q are integers and q≠ 0. Rational Numbers Example Collection of rational number is denoted by “Q” 10 RationalNumbers
• 11. 11 Number Systems Some Important Points:-  Every integer, whole and natural number is a rational number.  Number of rational numbers between two rational numbers is infinite.  Suppose a and b are two rational numbers, then a x b a + b = Rational Number a + b a ÷ b (where b is non-zero i.e. b ≠ 0) Closure property under addition, subtraction, multiplication and division is satisfied by rational numbers. RationalNumbers
• 12. Number Systems Irrational Numbers All numbers which cannot be written in p/q form, where p and q are integers and q≠ 0 IrrationalNumbers Example 12 Square roots of all positive integers are not irrational e.g. 9 = 3 (rational number)
• 13. 13 Number Systems Some Important Points:-  Irrational numbers have non-terminating and non-repeating decimal expression.  Irrational numbers can be easily represented on number line by using Pythagoras Theorem where In right angled ∆[Hypotenuse]2 = [Base]2 + [Perpendicular]2  Suppose a and b are two irrational numbers, then a x b a + b = Not always an Irrational Number a + b a ÷ b Closure property under addition, subtraction, multiplication and division is not satisfied by irrational numbers. Irrational Numbers
• 14. 14 RATIONAL NUMBER TERMINATING or NON- TERMINATING RECURRING DECIMAL EXPANSION DECIMAL EXPANSION IRRATIONAL NUMBER NON-TERMINATING or NON-RECURRING DECIMAL EXPANSION DECIMAL EXPANSION Number Systems Decimal Expansion
• 15. 15 Number Systems Real Numbers Real numbers include all rational and all irrational numbers. Denoted by ‘R’ RealNumbers THE REAL NUMBER LINE
• 16. 16 IRRATIONAL NUMBERS RATIONAL NUMBERS REAL NUMBERS NATURAL NUMBERS INTEGERS WHOLE NUMBERS So…What we learned today Number Systems
• 17. 17 Number Systems RealNumbers Real Numbers :-  Both rational and irrational numbers together makes a collection of real numbers.  On a number line, there is a unique real number corresponding to every point and also corresponding to each real number there is a unique point.  Suppose we have one rational and one irrational number, then:- Rational Number + Irrational Number = Irrational Number Rational Number - Irrational Number = Irrational Number Rational Number x Irrational Number = Irrational Number, Rational Number ≠ 0 Rational Number / Irrational Number = Irrational Number, Rational Number ≠ 0 Real numbers also satisfy the various laws i.e. commutative, associative and distributive laws etc.
• 18. 18 Number Systems Thanksfor watching…YRS2.Learning s one stop source that helps both students and teachers through their entire educational journey from class I to 10th. Our prompt, complete, accurate and self-explanatory visual presentation of the concepts saves your precious time and energy. Hope it helped you! If yes do like us & subscribe our channel for more. For any query or suggestion, drop us an email at: yrs2.learning@gmail.com