Powerpoint real numbers
- 2. REAL NUMBERSREAL NUMBERS S b itt d bSubmitted by Sh YShareena .Y M th tiMathematics R N 18014350013Reg.No. 18014350013
- 3. Real NumbersReal Numbers The set of Real Numbers consists of all rational and irrational numbers.
- 4. E l f R lExamples of Real NumbersNumbers 1 11 1 2,2, , , 2, 3, 5,............. 2 3 2 3
- 5. Properties of Real NumbersProperties of Real Numbers The sets N, Z,Q and Q are subsets of RThe sets N, Z,Q and Q are subsets of R N-Natural Number, Z – Integers R Rational Numbers Q Irrational NumbersR- Rational Numbers, Q - Irrational Numbers R – Real Numbers l b iBetween any two real numbers we can write as many real numbers as we alike. The set of real numbers is closed under addition, subtraction, multiplication, division (except division b )by zero)
- 6. Real Numbers Rational Numbers Irrational Numbers Integers Non Negative Positive integers Negative Positive Negative Integers Zero N t l Negative Positive Natural numbers
- 7. Rational NumbersRational Numbers A b hi h b P A number which can be expressed in the form of p q expressed in the form of p, P/q where p,qz and q 0P/q where p,qz and q 0 is called a rational number
- 8. Examples of Rational NumbersExamples of Rational Numbers 3 is a rational number since 633 is a rational number since, where 6,2z and 2 0. 63 2 is a rational number since 3,5z d 5 0 3 5 and 5 0. is a rational number since ‐2,3z2 is a rational number since 2,3z and 3 0 2 3
- 9. Equivalent Rational NumbersEquivalent Rational Numbers The rational numbers do not have aThe rational numbers do not have a unique representation in the formq p where p and q are integers andP q q 0. 1 2 1 0 3 0 1 31 2 1 0 3 0 1 3: 2 4 2 0 6 0 2 6 e g
- 10. Irrational NumbersIrrational Numbers Numbers which are not rational butNumbers which are not rational but which can be represented by points on th b li ith th ti lthe number line with the rational numbers are called irrational numbers. In other words, a number ‘s’ is called irrational, if it cannot be written in theirrational, if it cannot be written in the form p/q, where p and q are integers and q0and q0.
- 11. Examples of irrational p numbers 1 12 2 2 3 51 12 ,2 , , , 2 , 3 , 5.......... 2 3 are irrational numbers.