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2-2 Powers of Ten and Scientific Notation

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					 2-2 Powers of Ten and Scientific Notation




Course 2
 2-2 Powers of Ten and Scientific Notation


    Warm Up
    Find each value.

    1. 92      81      2. 122     144
    3. 152    225      4. 102     100
    5. 103   1,000     6. 104   10,000




Course 2
 2-2 Powers Lesson Title Here Notation
     Insert of Ten and Scientific

                  Vocabulary
Standard Form: a way to write numbers by using digits.
     Example: three hundred sixty five in
            standard notation is 365.
Scientific Notation: a method of writing very large or
  very small numbers by using powers of 10.




Course 2
 2-2 Powers of Ten and Scientific Notation



           The distance from Venus to the Sun is over
           100,000,000 kilometers. You can write this
           number as a power of ten by using a base of
           ten and an exponent.


           10 · 10 · 10 · 10 · 10 · 10 · 10 · 10 = 108
                                Power of ten




Course 2
 2-2 Powers of Ten and Scientific Notation


       The table shows several powers of ten.

           Power of 10       Meaning         Value

               101              10            10

               102            10 · 10        100

               103         10 · 10 · 10      1,000

               104       10 · 10 · 10 · 10   10,000



Course 2
 2-2 Powers of Ten and Scientific Notation

           Example 1: Multiplying by Powers of Ten


    Multiply 14 · 103.

           14 · 103 = 14 · (10 · 10 · 10)   Use 10 as a factor
                                            3 times.
                   = 14 · 1,000             Multiply.
                   = 14,000




Course 2
 2-2 Insert Lesson Title Here Notation
     Powers of Ten and Scientific

                      Try This: Example 1


    Multiply 12 · 102.

           12 · 102 = 12 · (10 · 10)   Use 10 as a factor
                                       2 times.
                   = 12 · 100          Multiply.
                   = 1,200




Course 2
 2-2 Powers of Ten and Scientific Notation



           You can also find the product of a number
           and a power of ten simply by moving the
           decimal point of the number. For powers of
           ten with positive exponents, move the
           decimal point to the right.




Course 2
 2-2 Powers of Ten and Scientific Notation

   Example 2: Multiplying by Powers of Ten Mentally

    Find each product.
      A. 212 · 104                  4 places

           212 · 104 = 212.0000      Move the decimal point
                                     4 places.
                      = 2,120,000    (You will need to add
                                      4 zeros.)
      B. 31.6 · 103
                                    3 places
           31.6 · 103 = 31.600        Move the decimal point
                                      3 places.
                      = 31,600        (You will need to add
                                      2 zeros.)
Course 2
 2-2 Insert Lesson Title Here Notation
     Powers of Ten and Scientific

                      Try This: Example 2

    Find each product.
      A. 22.5 · 102              2 places

           22.5 · 102 = 22.50      Move the decimal point
                                   2 places.
                      = 2,250      (You will need to add
                                    1 zero.)
      B. 39.5 · 103
                                 3 places
           39.5 · 103 = 39.500     Move the decimal point
                                   3 places.
                      = 39,500     (You will need to add
                                   2 zeros.)
Course 2
 2-2 Powers of Ten and Scientific Notation

      Numbers are usually written in standard form.
      For example, 17,900,000 is in standard form.
      Scientific notation is a kind of shorthand that
      can be used to write large numbers. Numbers
      expressed in scientific notation are written as the
      product of two factors. In scientific notation,
      17,900,000 is written as




    A number greater                        A power of 10
    than or equal to 1 but
    less than 10
Course 2
 2-2 Powers of Ten and Scientific Notation




       Writing Math
       In scientific notation, it is customary to use
       a multiplication cross () instead of a dot.




Course 2
 2-2 Powers of Ten and Scientific Notation

 Example 3A: Writing Numbers in Scientific Notation

    Write the number in scientific notation.
      A. 4,340,000           6 places

                             Move the decimal point to
      4,340,000 = 4,340,000 get a number that is greater
                             than or equal to 1 and less
                             than 10.
                              The exponent is equal to
                = 4.34  106
                              the number of places the
                              decimal point is moved.


Course 2
 2-2 Powers of Ten and Scientific Notation

 Example 3B: Writing Numbers in Scientific Notation
    Write the number in scientific notation.

      B. 327,000,000      8 places
                          Move the decimal point to
327,000,000 = 327,000,000 get a number that is greater
                          than or equal to 1 and less
                          than 10.

                              The exponent is equal to
             = 3.27    108   the number of places the
                              decimal point is moved.


Course 2
 2-2 Insert Lesson Title Here Notation
     Powers of Ten and Scientific

                 Try This: Example 3A
    Write the number in scientific notation.
      A. 8,421,000            6 places

                              Move the decimal point to
    8,421,000 = 8,421,000     get a number that is greater
                              than or equal to 1 and less
                              than 10.
                               The exponent is equal to
              = 8.421  106
                               the number of places the
                               decimal point is moved.


Course 2
 2-2 Insert Lesson Title Here Notation
     Powers of Ten and Scientific

                Try This: Example 3B
    Write the number in scientific notation.

      B. 327,000              5 places

                               Move the decimal point to
      327,000 = 327,000        get a number that is greater
                               than or equal to 1 and less
                               than 10.

                               The exponent is equal to
             = 3.27    105    the number of places the
                               decimal point is moved.

Course 2
 2-2 Powers of Ten and Scientific Notation

      Example 4: Writing Numbers in Standard Form

    The population of China in the year 2000 was
    estimated to be about 1.262  109. Write this
    number in standard form.
                                    Since the
      1.262  109 = 1.262000000
                                    exponent is 9,
                                    move the decimal
                                    point 9 places to
                                    the right.
                  = 1,262,000,000

    The population of China was about 1,262,000,000
    people.
Course 2
 2-2 Insert Lesson Title Here Notation
     Powers of Ten and Scientific

                      Try This: Example 4
    The distance from the Earth to the Sun is
    calculated to be 1.5  108 kilometers. Write
    this distance in standard form.
       1.5  108 = 1.50000000         Since the exponent is
                                      8, move the decimal
                                      point 8 places to the
                                      right.
                    = 150,000,000


           The distance from the Earth to the Sun is about
           150,000,000 kilometers.
Course 2
 2-2 Powers Lesson Title Here Notation
     Insert of Ten and Scientific

      Assignment:
           pg. 66 14-39
              Left Column Only




Course 2

				
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