Scientific Notation, Exponents and Significant Figures by kzp12233

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									   Scientific Notation,
Exponents and Significant
        Figures
               Scientific Notation
   Scientific Notation – It is notation used to
    express very large or very small numbers
    using powers of 10.
       It is written as a number multiplied by 10x
          Example: 1000 = 1 x 103 (10 x 10 x 10)
          Here the 1000 is in standard notation

          1 x 103 is scientific notation
              Scientific Notation
   How do we express these terms?
   For Scientific Notation:
       The number is expressed as >1 and <10 and
        then multiplied by a power of 10.
   Example: 523,000 = 5.23 x 105
        Scientific Notation
Prefix Symbol Standard notation   Exponent
giga-    G      1 000 000 000        109
mega-    M        1 000 000          106
 kilo-   k           1000            103
deci-    d            0.1           10-1
centi-   c           0.01           10-2
milli-   m          0.001           10-3
micro-   µ        0.000 001         10-6
nano-    n      0.000 000 001       10-9
pico-    p    0.000 000 000 001     10-12
             Scientific Notation
   So, how do we change from standard
    notation to scientific notation?
   Move the decimal point to create number
    that is between 1 and 10
       Example: 7,231,967 = 7.231967 x 106

                 0.00003433 = 3.433 x 10-5
              Scientific Notation
   Rules:
       The decimal place should end up at to the
        right of the first nonzero digit.
       The total number of spaces moved becomes
        the exponent of 10 in the scientific notation.
       If the given number is greater than 1, the
        exponent is positive.
       If the given number is less than 1 (but >0),
        the exponent is negative.
             Scientific Notation
   Practice writing these in scientific notation.
   17 mL
   153 kg
   24883.5 km
   2000 miles
   0.4502 g
   0.00063401 m
            Scientific Notation
   You can also use this information to write
    a number in standard notation.
   Example: 2.3445 x 103 g= 2344.5 g
             2.21 x 10-7 m = 0.000000221 m
             Scientific Notation
Practice: Write the follow ing in standard notation:
 6.423 x 103 g             6423 g



   1.002 x 10-6 m           0.000001002 m

   5.0023 x 1010 m          50,023,000,000 m

   3.3 x 10-9 sec           0.0000000033 sec
           Rules of Exponents
   Remember that exponents, especially with
    powers of 10, help count zeros.
   It is easier to see keep track of zeros with
    and exponent like 106 than with the
    standard notation of 1,000,000.
   Using the rules of exponents, you can
    multiply and divide exponents easily.
                   Exponents
   Rules of Exponents        Example
      (10m)(10n) = 10m+n      (102)(103 100,000
                             100*1000)== 105

      (10m)n = 10m*n          (103)2 = 106
                             (1000)2 = 1,000,000

      10m/10n = 10m-n       106/102 = 10410,000
                                1,000,000 =
                                   100
       10-m = 1/10m          10-8 = 1/108
                                 1      = 0.00000001
                            100,000,000
       100 = 1                         = 1 x 10-8
Scientific Notation & Exponents
Prefix Symbol Standard notation   Exponent
giga-    G      1 000 000 000        109
mega-    M        1 000 000          106
 kilo-   k           1000            103
deci-    d            0.1           10-1
centi-   c           0.01           10-2
milli-   m          0.001           10-3
micro-   µ        0.000 001         10-6
nano-    n      0.000 000 001       10-9
pico-    p    0.000 000 000 001     10-12
Scientific Notation & Exponents
Practice:
 Convert numbers or exponents to prefix.

 1000 g              1 x 103 g or 1 kg

 5.3 x 103 m         5.3 km

 4.5 x 10-6 m        4.5 µm

 1.7 x 10-3g         1.7 mg

 22000 seconds       22 kiloseconds
Scientific Notation & Exponents
   2.4 mg                      2.4 x 10-3 g
   2 km                        2 x 103 m
   1.6 Mm (megameter)          1.6 x 106 m
   15 msec (milliseconds)      (1.5 x101) x 10-3 sec
                                 or 1.5 x 10-2 sec
   253 km                      (2.53 x 102) x 103 m
                                Or 2.53 x 105 m
                Exponents
   How many milligrams are in a kilogram?
   1 kg = 1000 g = 103 g x 1 mg =
                            10-3g

                               = 106 mg
                  Exponents
   How many picograms in a microgram?
       1 µg = (1 x 10-6 g)(1 pg     )=
                          1x10-12 g
               1/(1 x 10-6) pg =
                   106 pg = 1,000,000 pg
             Significant Figures
   With scientific measurements, you want to
    know accuracy, precision and certainty.
       Accuracy – How close a measurement is to an
        accepted value
       Precision – How close a measurement is to
        other measurements of the same thing.
       Certainty – Degree of confidence of a
        measurement. The last digit to the right is
        usually an uncertain digit.
           Significant Figures
   So for any measured value, we’ll record all
    of the certain digits plus an uncertain
    digit.
   All together, they are the significant
    figures of the measurement.
     Significant Figure RULES
1. All non zero digits (1,2,3,4,5,6,7,8, and 9) are
   significant.
2. Final zeros to the right of the decimal point are
   significant.
3. Zeros between two significant digits are
   significant.
4. Zeros used for spacing the decimal point are
   not significant.
5. For numbers in scientific notation, all of the
   digits before the “x 10x” are significant.
    How Many Significant Figures?
         Measurement                 # of Sig Figs
   135.3                 4   sig   figs
   4.6025                5   sig   figs
   200,035               6   sig   figs
   0.0000300             3   sig   figs
   2.0000300             8   sig   figs
   0.002                 1   sig   fig
   4.44 x 103            3   sig   figs
   2.0 x 10-2            2   sig   figs
   10.00                 4   sig   figs
   10                    1   sig   fig
   102,000               3   sig   figs
             Significant Figures
Multiplying and Dividing with Sig Figs
   When multiplying or dividing measurements, the
    answer must have the same number of sig figs
    as the measurement with the fewest sig figs.
   Example: 22 feet x 9 feet = 198 square
    feet…but
   Since 9 feet only has 1 sig fig the correct answer
    is
                        200 ft2
Calculate the Area in square blocks




    3



    2



   1



    0     1     2    3     4      5
              Significant Figures
Calculation     Calc’d Answer   Ans w/sig figs
2.86 m x
  1.824 m       5.21664 m2      5.22 m2

460 miles/
   8 hours      57.5 mi/hr      60 mi/hr

98.50 in x
  1.82 in       179.27 in2      179 in2
             Significant Figures
Calculation    Calc’d Answer   Ans w/sig figs
2.100 m x
  0.0030 m     0.0063 m2       0.0063 m2

10.00 g /
   5.000 L     2 g/L           2.000 g/L

4.610 ft x
  1.7 ft       7.837 ft2       7.8 ft2
              Significant Figures
   Defined numbers – part of a definition and
    is not measured. So, defined numbers
    (unit conversion factors) do not limit the
    sig figs in an answer.
   Also, counting numbers do not limit sig
    figs.
       Example: You cut a 24 ft piece of wood into 4
        pieces. Each is 24 ft/4 = 6.0 ft/piece.
              Significant Figures
   Addition and Subtraction
       The sig figs with addition and subtraction are
        handled differently than with x and /.
       The answer cannot have more certainty than
        the least certain measurement.
       This means the answer must have the same
        number of sig figs to the right of the decimal
        as the measurement with the fewest sig figs
        to the right of the decimal place.
         Significant Figures
Example:
    4.271 g (3 sig figs to right of decimal)
    2     g (0 sig figs to right of decimal)
   10.0 g (1 sig fig to right of decimal)
   16.271 g is calculated answer but…
     since 2 g has no sig figs to right of
      decimal the final answer is 16 g.

								
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