The Real Number System Essential Question: -How do we classify numbers as rational or irrational?

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Presentation transcript:

The Real Number System Essential Question: -How do we classify numbers as rational or irrational?

Understanding Rational and Irrational “Makes Sense” “Doesn’t Make Sense” Rational Numbers Irrational Numbers -Any number that can be written as a fraction. -Non-terminating and non-repeating decimals. fractions -can’t be written as a fraction. wholes integers terminating decimals repeating decimals

Sets of Numbers Naturals - Natural counting numbers. { 1, 2, 3… } { 1, 2, 3… } Wholes - Natural counting numbers and zero. { 0, 1, 2, 3… } Integers - Positive or negative natural numbers or zero. { … -3, -2, -1, 0, 1, 2, 3… } Rationals - Any number which can be written as a fraction. Irrationals - Any decimal number which can’t be written as a fraction. A non-terminating and non-repeating decimal. Reals - Rationals and irrationals.

…-3, -2, -1, 0, 1, 2, 3... …-3, -2, -1 Sets of Numbers Reals Rationals Irrationals - any number that can be written as a fraction. - non-terminating and non-repeating decimals , 7, -0.4 Fractions/Decimals Integers , -0.32, - 2.1 …-3, -2, -1, 0, 1, 2, 3... Negative Integers Wholes …-3, -2, -1 0, 1, 2, 3... Zero Naturals 1, 2, 3...

Sets of Numbers This is a Venn Diagram that displays the following sets of numbers: Naturals, Wholes, Integers, Rationals, Irrationals, and Reals. Reals Rationals -2.65 Integers -3 -19 Wholes Irrationals Naturals 1, 2, 3...

Identify each number below as natural, whole, integer, rational, irrational, or real. More than one may apply. Rational , Real Whole , Integer , Rational , Real Integer , Rational , Real Irrational , Real Natural ,Whole , Integer , Rational , Real

Identify each number below as natural, whole, integer, rational, irrational, or real. More than one may apply. Rational , Real Integer , Rational , Real Natural ,Whole , Integer , Rational , Real Integer , Rational , Real Irrational , Real