Scientific Notation and Significant Figures

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					Bell Ringer: Oct. 4, 2010:
Complete the table below. Place X in the appropriate
box to indicate the type of each measurement unit.
Reference: Physical Science, page 16

     Measurement       SI Unit         Derived Unit
Gram per centimeter
cubed (g/cm3)
Decimeter (dm)
Liter (L)
Meter cubed (m3)
Kilogram (kg)
   Glenn C. Soltes
Integrated Science
           Biology
         2010-2011
Objectives:
 Define Scientific Notation and Significant Figures.
 Identify the rules in writing scientific notation and
  significant figures.
 Use scientific notation and significant figures in
  problem solving.
 Identify the significant figures in calculations.
Scientific Notation

         A short-hand way of writing large
 numbers without writing all of the zeros.
A number is expressed in scientific
    notation when it is in the form
                             a x 10n
       where a is between 1 and 10
               and n is an integer
The Distance From the Sun to the
Earth


        93,000,000 miles
 Write the width of the universe in
 scientific notation.
210,000,000,000,000,000,000,000 miles
     Where is the decimal point now?
           After the last zero.
Where would you put the decimal to make
     this number be between 1 and 10?
         Between the 2 and the 1
2.10,000,000,000,000,000,000,000.
How many decimal places did you move
 the decimal?
                     23
 When the original number is more than
        1, the exponent is positive.
   The answer in scientific notation is
                 2.1 x 1023
 Write 28750.9 in scientific notation.
1.   2.87509 x 10-5
2.   2.87509 x 10-4
3.   2.87509 x 104
4.   2.87509 x 105
2) Express 1.8 x 10-4 in decimal
notation.
                 0.00018
    3) Express 4.58 x 106 in decimal
                 notation.
               4,580,000
  On the graphing calculator, scientific
  notation is done with the      button.
      4.58 x 106 is typed 4.58    6
Practice Problem
     Write in scientific notation.
     Decide the power of ten.




1) 98,500,000 =
2) 64,100,000,000 =
3) 279,000,000 =
4) 4,200,000 =
5) .000567 =
 A prescribed decimal place that determines the
amount of rounding off to be done based on the
                 precision of the measurement.
There are 2 kinds of
numbers:
Exact: the amount of
 money in your account.
 Known with certainty.
Approximate: weight,
 height—anything
 MEASURED.
No measurement is
 perfect.
When a measurement
is recorded only those
digits that are
dependable are
written down.
If you measured the
 width of a paper with
 your ruler you might
 record 21.7cm.
To a mathematician
 21.70, or 21.700 is the
 same.
But, to a scientist 21.7cm and
21.70cm is NOT the same
 21.700cm to a scientist
  means the
  measurement is
  accurate to within one
  thousandth of a cm.
If you used an ordinary
ruler, the smallest
marking is the mm, so
your measurement has
to be recorded as 21.7cm.
Rule: All digits are
significant starting
with the first non-zero
digit on the left.
Exception to rule: In
whole numbers that
end in zero, the zeros
at the end are not
significant.
How many significant
figures?
7            1
40           1
0.5          1
0.00003      1
7 x 105      1
7,000,000    1
2ndException to rule:
If zeros are
sandwiched between
non-zero digits, the
zeros become
significant.
How many significant figures
here?
1.2             2
2100            2
56.76           4
4.00            3
0.0792          3
7,083,000,000   4
How many sig figs here?
3401            4
2100            2
2100.0          5
5.00            3
0.00412         3
8,000,050,000   6
Practice: Count the number of
significant figures.
1. 80000
2. 0.0015
3. 8 002 000
4. 1.12
5. 1.oo5
Rule: When adding or
subtracting measured
numbers, the answer can
have no more places after
the decimal than the LEAST
of the measured numbers.
Add/Subtract examples
2.45cm + 1.2cm = 3.65cm,
Round off to    = 3.7cm

7.432cm + 2cm = 9.432
 round to        9cm
Multiplication and Division
 Rule: When
  multiplying or
  dividing, the result
  can have no more
  significant figures
  than the least reliable
  measurement.
A couple of examples
56.78 cm x 2.45cm = 139.111 cm2
Round to          139cm2


75.8cm x 9.6cm = ?
Perform the following calculations, and write the answer
with the correct number of significant figures.
 a. 12.65 cm x 42.1 cm
 b. 3.02 cm x 6.3 cm x 8.225 cm
 c. 3.7 g ÷ 1.o83 cm3
          Credit:
Holt, Physical Science 2006

				
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posted:8/13/2012
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