Rational and irrartional numbers

WELCOME

COMMON NATURE & PECULARITIES OF RATIONAL &

IRRATIONAL NUMBERS

PRESENTED BY ASWATHY S MATHEMATICS OPTIONAL KERALA UNIVERSITY COLLEGE

OF TEACHER EDUCATION KUMARAPURAM THIRUVANANTHAPURAM

WHAT IS A RATIONAL NUMBER?

INTEGERS AND FRACTIONS ARE COLLECTIVELY CALLED RATIONAL NUMBERS.

WHAT IS AN IRRATIONAL NUMBER?

4

NUMBERS WHICH ARE NOT RATIONAL ARE CALLED IRRATIONAL NUMBER.

WHAT DO YOU MEAN BY REAL NUMBERS ?

RATIONAL AND IRRATIONAL NUMBERS TOGETHER WITH THEIR NEGATIVES AND ZERO ARE COLLECTIVELY CALLED REAL NUMBERS.

CLASSIFICATION OF REAL NUMBERS

SIMPLE REPRESENTATION OF REAL NUMBERS

COMMON NATURE AND PECULARITIES OF RATIONAL AND

IRRATIONAL NUMBERS1)ALL POSITIVE RATIONAL NUMBERS CAN BE VISUALISED AS LENGTHS.

2)ALL POSITIVE IRRATIONAL NUMBERS CAN BE VISUALISED AS LENGTHS.

3)THERE ARE SO MANY RATIONAL NUMBERS BETWEEN 0 AND 1.

4)THERE ARE MANY IRRATIONAL NUMBERS BETWEEN 0 AND 1.

5)RATIONAL NUMBERS ARE CHANGED INTO ENDING OR RECURRING DECIMALS.THE APPROXIMATE VALUE OF RATIONAL NUMBERS CAN BE WRITTEN IN THE DECIMAL FORM.

6)THE APPROXIMATE VALUE OF IRRATIONAL NUMBERS CAN ALSO BE WRITTEN IN THE DECIMAL FORM.

7)ALL RATIONAL AND IRRATIONAL NUMBERS TOGETHER CALLED REAL NUMBERS.

SUMMARY

THE COMMON NATURE AND PECULIARITIES OF RATIONAL & IRRATIONAL NUMBERS CONSTITUTE THE SAME PROPERTIES IN REAL NUMBERS ALSO.

CLASS ASSIGNMENT

1)IS THE SQUARE OF ANY FRACTION EQUAL TO TWO? ANS: (1)^2+ (1)^2=2,SO WHAT IS THE DIAGONAL?

LENGTH OF THE DIAGONAL=SQUARE ROOT OF TWO.IN OTHER WORDS SQU.OF 1 IS 1, SQU.OF 2 IS 4,2 IS BETWEEN 1 &4.THERE IS NO NATURAL NUMBER BETWEEN 1&2.SO, NO NATURAL NUMBER HAS SQUARE 2 .

2)FIND THE PERIMETER OF THE TRIANGLE SHOWN BELOW? (HINT:GIVEN THATBASE=3cm,altitude=2cm)

ANS: SINCE IT IS A RIGHT TRIANGLE,WE CAN CALCULATE HYPOTENUSE USING PYTHAGORUS THEOREM,BASE^2+ ALT.^2=HYP.^2SO HYPO.=SQUARE ROOT OF 13cm

PERIMETER=2+3+SQUARE ROOT OF 13

=5+SQUARE ROOT OF 13cm

SQUARE ROOT OF 13=3.6055..........

SINCE IT IS DIFFICULT TO MEASURE

LENGTHS LESS THAN A MILLIMETRE,WE

NEED ONLY TAKE THE FIRST DECIMAL

PERIMETER=8.6cm approximately

HOME ASSIGNMENT

“FIND THE PERIMETER OF A SQUARE OF AREA 10 SQUARE METRES?

THANK YOU…,