# 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
   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
   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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