8-31 Math 9 Cornell notes – Rationals, Irrationals, and Reals

8-31 Math 9 Cornell notes – Rationals, Irrationals, and Reals

Today each table studied statements such as pi = 3.14 and 1/3 = .3

Then they gave presentations on which statements were true.  Some of the statements had the dotted equal sign which means “approximately equal to” or “almost equal to.”

(drawing of N, W, I circles inside the Rational rectangle)	The decimal equivalents of rational numbers -          Can terminate (end), such as ½ = .5 and 3/8 = .375 -          Can repeat, such as 2/3 = .66666 . . . and 1/13 = .076923076923. . . -          The “. . .” symbol is an ellipsis.  It means the idea keeps going. Some square roots, such as those of perfect squares, are rational, such a SQRT (36) = 6
(add the Irrational rectangle to the N, W, I, R drawing)	The decimal equivalents of irrational numbers        -      Never end        -      Never repeat For example, pi = 3.141592654 . . . And SQRT(2) = 1.414213562. . . Example:  SQRT (3) = 1.732050808. . . Example:  e = 2.71828. . .
(drawing of the large Real rectangle which includes the Rational and Irrational rectangles)	Rational numbers combined with Irrational numbers are the Set of Real numbers. None of the N, W, or I numbers is in the Irrational rectangle
Write an Irrational number	Take all the odd numbers:  1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, . . . Strike out the perfect squares:     3, 5, 7, , 11, 13, 15, 17, 19, 21 23, , 27. . . Take the square root of any of the remaining numbers. Example:  SQRT (23) = 4.795831523. . . is irrational. Example:  SQRT (7) = 2.645751311. . . is irrational.