* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download NUMBER SYS LEC -1
Survey
Document related concepts
Numbers (TV series) wikipedia , lookup
History of logarithms wikipedia , lookup
Law of large numbers wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Ethnomathematics wikipedia , lookup
Infinitesimal wikipedia , lookup
Location arithmetic wikipedia , lookup
Foundations of mathematics wikipedia , lookup
Georg Cantor's first set theory article wikipedia , lookup
Bernoulli number wikipedia , lookup
Surreal number wikipedia , lookup
Positional notation wikipedia , lookup
Large numbers wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
Real number wikipedia , lookup
Transcript
J E E (Mathematics) Class IX Number System 7 3 and on real number line. 3 7 – For 3 : 7 For 7 3 Q P O –7 –6 –5 –4 –3 –2 –1 0 Divide segment OA into 7 equal parts count 3 parts from 0 3 : 7 3 7 A B C 1 2 3 Divide equal segment OP, PQ into 3 equal parts Count 7 parts from 0 to left For mixed fraction convert to proper fraction first. EXAMPLE 3 : Represent 2 in IIT I N EET I B OARD S I FO UNDATIO N I OTH ERS EXAMPLE 2 : Represent N o n lin e p a d h o ... 3 on a number line 8 2 Q A B 0 1 2 3 3 2 8 2 8 To represent 2 3 3 : After 2 represent 8 8 Divide BC into 8 parts Count 3 parts B to C OR Represent 2 3 19 on number line like example 2. 8 8 3 8 C 3 JE E N in o n lin e p a d h o ... (Mathematics) Class IX Number System IIT I NEET I BOARDS I FOUNDATIONI OTHERS Irrational Numbers : If a number cannot be written in the form of p where p and q are integers and q 0, then the number is q called as irrational number. 2, 3 5 and 2 5 etc. Example : Real Numbers : Numbers which can represent actual physical quantities in a meaningful way are known as real numbers. Real numbers includes all rational and irrational numbers. Prime Numbers : All natural numbers which have 1 and itself only as their factors are called prime numbers. Example : 2, 3, 5, 7, 11, 13, 17, 19, ..... etc. Composite Numbers : All natural numbers which are not prime are composite numbers. Co-prime Numbers : If HCF of given numbers is 1, then they are co-primes. Example : 4 and 9 Any two consecutive numbers will always be co-primes. Imaginary Numbers : All the numbers that have their square is negative are called imaginary numbers. Example : 3i, –2i, 1 etc. i 1 Rational Numbers : A rational number a a is positive if both a and b have same sign and is negative if both have b b opposite sign Every rational number can be expressed as either a terminating decimal or a recurring decimal. Every integer can be expressed as Example : 3 p , where q = 1. q 3 5 9 , 5 , 9 etc. 1 1 1 EXAMPLE 1 : State whether following statements are true/false. Give reason for your answer. (i) Every rational number is a whole number (F) (ii) Every whole number is an integer (T) (iii) Every rational number is an integer (F) Representing Rational Numbers On Number Line : In a rational number, the numeral below bar is denominator, represents the number of equal parts into which upper part i.e., numerator has been divided. Draw a line and mark a point 0 on it to represent number ‘0’ (zero). The positive rational numbers will be represented by points on right side of 0 and negative will be on left side of 0. (Mathematics) Class IX Number System J E E N o n lin e p a d h o ... in IIT I N EET I B OARD S I FO UNDATIO N I OTH ERS LECTURE # 01 INTRODUCTION : Natural Numbers : Counting numbers are called as natural numbers Natural numbers (N) = {1, 2, 3, 4, .....} Whole Numbers : If we include zero (0) to collection of natural numbers, then all together from whole numbers Whole numbers W = {0} + N W = {0, 1, 2, 3, 4, .....} Integers : If we include negative of natural numbers to collection of whole numbers then all together from collection of integers. I or Z = {....., –2, –1, 0, 1, 2, 3, .....} 0 is non-negative and non-positive integer (neither negative nor positive). Non-negative integers : 0, 1, 2, ..... Non-positive integers : ....., –3, –2, –1, 0 Rational Numbers : The numbers which can be expressed in the form of p , q 0 and q and p are integers. The set of rational q numbers is denoted by Q. 1 2 1 Q , , , ..... etc. 3 9 4 Note : All natural numbers, whole numbers and integers are rational. Q=N+Q+Z 1 2 10 and so on all are equivalent rational numbers. 2 4 20 Two rational numbers are said to be equivalent if we divide each decimal value will be the same. Difference Between Fraction And Rational Number : A fraction is a number that expresses part of a whole as a quotient of integers (denominator 0) or as a repeating or terminating decimal. So every fraction is a rational number but every rational number is not fraction. Example : 4 is rational but not a fraction 1 The fractions are a subset of the rational numbers The rationals contain the integers, and fraction don’t.