1. How do we know what’s what?

2.  A rational number is a number that can be written as a simple fraction ◦ Ex. 5 5/1  ◦ Ex. 0.3333333…1/3  ◦ Ex. 1.32567…?/? x  Formal definition: “ A rational number is a number that can be written in the form p/q where p and q are integers and q is not equal to zero” * Why can’t q be zero?

3. PQp/q=yes or no 111/11Yes 161/61.66666…Yes 5510055/1000.55Yes 25310253/1025.3Yes 707/0?No √913/13Yes √21 1.414213…No When looking at the decimals, what can we conclude about determining if it is a rational number? The decimal has to REPEAT or TERMINATE!

4. The ancient Greek mathematician Pythagoras believed that all numbers were rational (could be written as a fraction), but one of his students Hippasus proved (using geometry, it is thought) that you could not represent the square root of 2 as a fraction, and so it was irrational.

5. However Pythagoras could not accept the existence of irrational numbers, because he believed that all numbers had perfect values. But he could not disprove Hippasus' "irrational numbers theory" and so Hippasus was thrown overboard and drowned!

6.  An Irrational Number is a real number that cannot be written as a simple fraction. ◦ Irrational means not Rational  Ex. Π = 3.14159… Not Rational!  Ex. √3= 1.73205080… Not Rational! *Notice: These decimals cannot be written as a fraction!

7.  1/4  2.3333….  -45.32  7  0.873250  9.914701…

8. Rational Numbers Integers Whole Numbers Counting # Irrational Numbers

9.  Any Number that can be written as a fraction.  Terminating or repeating decimals  Fractions  Integers  Can be positive or negative  Examples: 0.33333…, 0.425, ½,- ¾, -2, 3.25, 0.2525252525….

10.  Positive and negative whole numbers  No fractions  No decimals  Zero IS included!  examples: …-3,-2,-1,0,1,2,3,…..

11.  No fractions  Not decimals  No negatives  Examples: 0,1,2,3,4,5,…..

12.  Aka counting numbers  Does not include zero  No negatives  No fractions  No decimals  Examples: 1,2,3,4,5,…..

13.  Any number that cannot be written as a fraction p/q  Non- repeating decimals  Non- terminating decimals  Examples: 1.34567231...., √2, π

14.  Name the numbers systems that each of the following numbers belongs to. -3 2/3 0.324… 23  Integers, Rational numbers  Rational numbers  Irrational numbers  Counting numbers, Whole numbers, Integers, Rational numbers

15.  It’s Simple!  Divide the numerator by the denominator  Ex 3/7 = 3÷ 7 = 0.42857143  Round to the nearest hundredth = 0.43

16.  Change the decimal to a fraction by using the given digits as the numerator and the place value as the denominator 0.125 = 125 / 1,000  Then we reduce the fraction! 125/1,000 = 1/8