Types of numbers.pptx

what are the types of numbers all numbers are covered in great detail as well as tables of associative, communicative and distributive properties explained in detail

1. Types of numbers -An informative presentation by Pranjal Garg

2. World of numbers! There are so many different types of numbers around us! Starting from simple natural numbers like 1,2,3.etc to very complex numbers such as 23+5i, 23i+687,etc. All of them play a vital role in carrying out various sophisticated mathematical calculations which help our lives become simpler and even better. How are these numbers classified into different types, what are the numerous properties associated with these numbers and where all these numbers actually come into use, are some of the questions we will be finding the answers for.

3. Types of numbers These infinite set of numbers are broadly classified into two groups- Real Numbers and Imaginary numbers.  These classifications help us better understand these numbers by organizing them into different groups. We will try to understand each of them in detail with ample of examples.  At last, beautiful games would help us to test our knowledge of these numbers we would have learnt so far.

4. Real Numbers The numbers which have a unique point on our real number line and can always be represented on it.

5. Whole Numbers and Natural numbers  Natural numbers These are simple numbers starting from 1,2,3… and used for simple counting All natural numbers are whole numbers. They are represented by the symbol N . Whole Numbers When zero is added to the collection of Natural numbers, they are known as whole numbers. All whole numbers are not natural numbers as they include zero with them. They are represented by the symbol W .

6. Properties of Whole numbers- Whole Numbers​​ ​​ Addition  ​​ Multiplication  ​​ Subtraction​​ Division​​ Closure   Property​​ ​​ Yes ​​ Yes ​​ No ​​ No Commutativity​​ ​​ Yes Yes No No Associativity  ​​ Yes Yes No No

7. Integers

8. Properties of Integers- Integers ​ Addition  ​ Multiplication  ​ Subtraction​ Division​ Closure   Property​ ​Yes Yes Yes No Commutativity​ ​Yes Yes No No Associativity  ​ Yes Yes No No

9. Rational Numbers These are the numbers between any two integers. They help us denote both positive and negative fractional values. Any number that can be written in the form of p/q and q There are infinitely many Rational numbers between any two given integers. They are represented by the symbol Q . For example- , etc.  

10. Properties of Rational numbers- Rational Numbers​​ ​​ Addition  ​​ Multiplication  ​​ Subtraction​​ Division​​ Closure   Property​​ ​​ Yes Yes Yes No Commutativity​​ Yes Yes No No Associativity  ​​ ​​Yes Yes ​​No No

11. Irrational Numbers Any number that cannot be written in the form of p/q and q These are present on the number line but an exact location of these cannot be determined as they never fit on the demarcations or divisions present on the number line. Thus, their decimal expansion go on forever without showing any specific pattern. Therefore, they cannot be represented in the form of p/q and q . For example- 23.468466545…. , 644.10100100011000001……  

12. Identifying Rational and Irrational numbers. Rational numbers Though they are non- terminating, they always show a definite pattern in their decimal expansions. Thus, they are characterized by either terminating or non-terminating but repeating. Irrational numbers These never terminate nor show any definite pattern in their decimal expansions. Thus, they are characterized by non-terminating and non-repeating. How do we come to know about whether a number is rational or irrational by just looking at their decimal expansions? Both of them have non- terminating decimal expansions. We can differentiate them as follow-

13. Games on Types of Numbers Game-1 Race your car

14. Question- 1 3,55,767,0 Give the type of numbers.

15. Solution - 1 Whole Numbers

16. Question- 2 3/5 , 3.55, 56, 7.888, -56.66 Give the type of numbers.

17. Solution - 2 Rational Numbers

18. Question- 3 5/3,34.67828…. , 0, 12.343434…., -4.66 ,etc. Give the type of numbers.

19. Solution - 3 Real Numbers

20. Question- 4 -435, 5 , -45, -2, 67 ,etc. Give the type of numbers.

21. Solution - 4 Integers

22. Question- 5 67i+45, 678i-46, 45i etc. Give the type of numbers.

23. Solution - 5 Complex Numbers

24. Question- 6 3.505005000…., 3.67235466…. etc. Give the type of numbers.

25. Solution - 6 Irrational Numbers