# Number system - Lecture 1

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This is the first class on Numbers and it covers Number tree and the definition of the different kinds of numbers.

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PowerPoint Presentation : Success Achievers Private Limited Number-System Lecture 1

PowerPoint Presentation : What is Number System?

PowerPoint Presentation : What is Number Tree?

PowerPoint Presentation : Why do I need to know Number tree? Is a fraction?

PowerPoint Presentation :

Real Numbers: : Real Numbers: All rational and irrational numbers together constitute real numbers. A number which can be represented on the number line is called as Real number and is denoted by R. ¾, 0.87, -90, 987, -4/9 The number line is an imaginary line with zero as origin, the nos on the right side of origin are called positive nos and the nos on the left side of the origin are called negative nos.

Complex Numbers: : Complex Numbers: A number of the form “a + bi” where ‘a’ and ‘b’ are real and b ≠0 is called a complex number. The ‘ i ’ represents iota or imaginary no. x 2 + 5 =0

Rational Numbers: : Rational Numbers: A rational number is the number which can be written in the form p/q and q ≠ 0. All integers and fractions can be written in the form of (p/q) and hence form rational numbers. Rational numbers are either terminating or recurring. Terminating nos : Numbers which terminates at some digit or decimal are called Terminating numbers. For eg ½, 45/90, 1/3, 7.8 Recurring nos : A decimal no in which a digit or a set of digits is repeated continuously is called a recurring decimal no. 1/3 = 0.3333….. 4/9 = 0.4444…..

Convert 0.44444….∞ to p/q form : Convert 0.44444….∞ to p/q form

Fundoo method : Fundoo method In general if we have a number N which is a recurring number comprised of Recurring (R) and Non-recurring number (NR), then the number can be written in the form of p/q as:

Irrational Numbers : Irrational Numbers A number which cannot be written in the form of p/q is called an irrational number. It is a number which is neither terminating nor recurring. Example: √3, π , 0.10112309……….

PowerPoint Presentation :

Integers: : Integers: All the counting numbers which have their denominator as 1 are called as integers. Example: -90, 67, 0, 999, 123, -87, 4/1 Consecutive integers: Consecutive integers are numbers differing by 1 in the ascending order. If two nos are consecutive, it is represented as ‘n’ and ‘n+1’. If 3 nos are consecutive, it is represented as ‘n-1’, ‘n’ and ‘n+1’

PowerPoint Presentation : Whole numbers: All counting nos including 0 are called whole numbers. Natural numbers: All whole nos excluding 0 are called natural nos. Natural nos can be classified as even nos and odd nos. Even nos are completely divisible by 2 and odd nos are natural nos not divisible by 2.

Properties of even and odd numbers: : Properties of even and odd numbers:

PowerPoint Presentation : If p is an even integer and q is an odd integer, which of the following must be an odd integer? a) p/q b) pq c) 2 p + q d) 2 ( p + q )

Prime numbers : Prime numbers Prime numbers are numbers which have got exactly two distinct factors. All prime numbers greater than 3 can be written in the form of 6k + 1 or 6k - 1. Example: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53…

Fundoo way of finding prime nos : Fundoo way of finding prime nos

PowerPoint Presentation : If ‘a’ and ‘b’ are prime nos , which of the following cannot be the sum of ‘a’ and ‘b’? a) 5 b) 9 c) 13 d) 23

PowerPoint Presentation : Thank You

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