Classifying Numbers

Rational Numbers vs.
 Irrational Numbers
A Rational Number:    An Irrational Number:

                     • Cannot be written as a
                       simple fraction
                     • Non-terminating decimal
                            (doesn’t end)
                     • Non-repeating decimal
                      (doesn’t repeat in a pattern)

                             Irrational doesn’t
                            mean that it’s crazy!



                                                    2
Examples of Rational
                  Numbers
             Click on each number to see explanation
                                                          Can be
 Can be                     Can be                       written as
written as                 written as                     7/1000
   3/1                        3/2




       Repeating
                                               Already in
      decimal. Can
                                             fraction form
      be written as           Can be
          1/9               written as 4
                             and as 4/1




                                                             3
Examples of Irrational
      Numbers




                         4
More Irrational Numbers
         Click on each number to see explanation
                     Remember . . .
Irrational numbers are non-repeating and non-terminating
      decimals and cannot be written as a fraction.
                                                Non-repeating
                                                decimal. Can’t
                                                be written as a
                                                   fraction




   Non-repeating
   decimal. Can’t
    be written as
      fraction




                                                        5
Try this . . .




                 6
Time to practice
                INCORRECT
           0.5 can be written as
                ½ and so it is
            rational. Try again!




                    Correct!
               0.5 can be written
                      as ½
                  Good work!




                                    7
Time to practice




                   8
Time to practice
                CORRECT!
               -5.060715…
           non-repeating, non-
           terminating decimal
                Good job!


                  INCORRECT
             -5.060715… appears
                  to be a non-
                repeating, non-
             terminating decimal
                   Try again!




                                   9
Time to practice




                   10
Time to practice
               INCORRECT
           2/3 is a fraction and
             so it is rational.
                 Try again!




                  CORRECT
               2/3 is a fraction.
                 Good work!




                                    11
Time to practice




                   12
How many RATIONAL
numbers can you find?




 Find the answer on the next slide
                                     13
Did you find
6 rational numbers?
     They are:




                      14

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Classifying Numbers

  • 1. Classifying Numbers Rational Numbers vs. Irrational Numbers
  • 2. A Rational Number: An Irrational Number: • Cannot be written as a simple fraction • Non-terminating decimal (doesn’t end) • Non-repeating decimal (doesn’t repeat in a pattern) Irrational doesn’t mean that it’s crazy! 2
  • 3. Examples of Rational Numbers Click on each number to see explanation Can be Can be Can be written as written as written as 7/1000 3/1 3/2 Repeating Already in decimal. Can fraction form be written as Can be 1/9 written as 4 and as 4/1 3
  • 5. More Irrational Numbers Click on each number to see explanation Remember . . . Irrational numbers are non-repeating and non-terminating decimals and cannot be written as a fraction. Non-repeating decimal. Can’t be written as a fraction Non-repeating decimal. Can’t be written as fraction 5
  • 6. Try this . . . 6
  • 7. Time to practice INCORRECT 0.5 can be written as ½ and so it is rational. Try again! Correct! 0.5 can be written as ½ Good work! 7
  • 9. Time to practice CORRECT! -5.060715… non-repeating, non- terminating decimal Good job! INCORRECT -5.060715… appears to be a non- repeating, non- terminating decimal Try again! 9
  • 11. Time to practice INCORRECT 2/3 is a fraction and so it is rational. Try again! CORRECT 2/3 is a fraction. Good work! 11
  • 13. How many RATIONAL numbers can you find? Find the answer on the next slide 13
  • 14. Did you find 6 rational numbers? They are: 14