Law vs. Theory, Scientific Notation, Significant Digits -Recognition by awt10412

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									          Law vs. Theory,
         Scientific Notation,
Significant Digits - Recognition and
           Operation rules
    Metric System Introduction
        Dimensional Analysis




                         Cartoon courtesy of NearingZero.net
                 Observations
   Quantitative Data
    ex: 3.0 mL 4.2 inches

   Qualitative Data
   ex: blue water smooth zinc

   What is the difference?
           Precision and Accuracy
       Accuracy refers to the agreement of a
    particular value with the true value.
    Precision refers to the degree of agreement
    among several measurements made in the same
    manner. Precision has another meaning also.




      Neither       Precise but not    Precise AND
    accurate nor       accurate          accurate
      precise
            Reading the Thermometer in
          Terms of Precision and Accuracy
     Determine the readings as shown below on Celsius
     thermometers:



Student A 44.0 oC Not Accurate, Precise
Student B 35 oC Not Precise , Accurate
Student C 54 oC Not Accurate Not Precise

The zero shows uncertainty in the
measurement.

                                       3 5 . _ C
                                       _ _ 0
      Reading the Thermometer
Determine the readings as shown below on Celsius
thermometers:




  8 7 4
  _ _ . _ C                  _ _ 0
                              3 5 . _ C
Why Is there Uncertainty in Measurements?
 Measurements are performed with instruments
 No instrument can read to an infinite number of
decimal places
A measurement always has some degree of
uncertainty.
  Which of these balances has the greatest
  uncertainty in measurement? The least uncertainty?
  Certain and Uncertain Digits are referred to as
                   Significant Digits!
 What are significant digits?

 All known digits (certain) and one estimated
  digit (uncertain)or (uncertain) place value.
 For electronic devices – record all digits. The
  estimation is already present.
 For non-electronic devices, an estimated place
  value must be obtained from reading the
  instrument.
                           The Thermometer
                         and Significant Digits.
                              o Determine the
                              temperature by reading
                              the scale on the
                              thermometer at eye
                              level.
                              o Read the temperature
                              by using all certain
                              digits and one uncertain
                              digit.
o Certain digits are determined from the calibration
marks on the thermometer.
o The uncertain digit (the last digit of the reading) is
estimated.
o On most thermometers encountered in a general
chemistry lab, the tenths place is the uncertain digit.
         Measuring Volume and
          Significant Digits
 Determine the volume contained in a graduated
cylinder by reading the bottom of the meniscus at
eye level.

 Read the volume using all certain digits and one
uncertain digit.

Together these are called significant digits.

 Certain digits are determined from the
calibration marks on the cylinder.

The uncertain digit (the last digit of the
reading) is estimated.
   Use the graduations to find all certain
   digits

There are two
unlabeled graduations
below the meniscus,
and each graduation
represents 1 mL, so
the certain digits of
the reading are… 52 mL.
  Estimate the uncertain digit and take a
  reading

The meniscus is about
eight tenths of the
way to the next
graduation, so the
final digit in the
reading is 0.8 mL .


   The volume in the graduated cylinder is 52.8 mL.
            10 mL Graduate
What is the volume of liquid in the graduate?



                                  6 6 2
                                  _ . _ _ mL
     100mL graduated cylinder
What is the volume of liquid in the graduated
cylinder?



_ _ 7
5 2 . _ mL
                Self Test
Examine the meniscus below and determine the
volume of liquid contained in the graduated
cylinder.

                          The cylinder contains:

                           7 6 . 0 mL
                           _ _ _
     25mL graduated cylinder
What is the volume of liquid in the graduate?




                               11 .5 0
                               _ _ _            mL
Why are significant digits needed?
   2nd meaning of precision.
        Significant digits express
              the sensitivity
        (divisions or calibration)
        of the measuring device.
                Balance Rules
In order to protect the balances and ensure accurate
results, a number of rules should be followed:
  Always check that the balance is level and zeroed
 (tared) before using it.
  Never weigh directly on the balance pan. Always
 use a piece of weighing paper or a weigh boat to
 protect it.
  Do not weigh hot or cold objects.
  Clean up any spills around the balance immediately.
 Remember, record all digits for electronic balances.
        Scientific Notation

In science, we deal with some very
LARGE numbers:
1 mole = 602000000000000000000000

In science, we deal with some very
SMALL numbers:
Mass of an electron =
0.000000000000000000000000000000091 kg
      Scientific Notation:
A method of representing very large or
  very small numbers in the form:
         M x 10n

    M is a number between 1 and 9
                1  M  10
   n is an integer
        2 500 000 000           .
           9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
         up so that one number is to its left
Step #3: Count how many places you bounce
         the decimal point
Step #4: Re-write in the form M x 10n
2.5 x   10 9


 The exponent is the
 number of places we
 moved the decimal.
         0.0000579
             1 2 3 4 5
Step #1: Locate the decimal point.

Step #2: Decide where the decimal must end
          up so that one number is to its left
Step #3: Count how many places you bounce
         the decimal point
5.79 x   10 -5


  The exponent is negative
  because the number we
  started with was less
  than 1.
 PERFORMING
CALCULATIONS
IN SCIENTIFIC
  NOTATION
Learn to use your
   calculator!
                    Remember: NO
   Locate the       GRAPHING
                    CALCULATORS!!!!
correct function
             Practice:
             ADD problems
  4 x 10 6

+ 3 x 10 6 Use your calculator
             for practice.
 7 x 106
  4 x 106
- 3 x 10 6

  1 x 106
A Problem for you…



    2.37 x   10 -4

  x 3.48 x 10-4


   8.30676 x   10-8
               Rounding Rule.

   5 or greater, round up
   Less than 5, round down
       Rules for Counting (Recognizing)
              Significant Digits
 for measurements Use Pacific/Atlantic Rules
          Pacific = Decimal Present
         Atlantic = Decimal Absent



RULE: Find the first nonzero number to the right
  or left of the arrow and every digit thereafter
  is significant.
   3456        has 4 sig digs.
   .0486       has 3 “    “
    9.000       has 4 sig dig.
   Underline the estimated digit.
       Rules for Significant Digits in
         Mathematical Operations

       Multiplication and Division: # sig digs
    in the result equals the number in the
    least precise measurement used in the
    calculation.

            6.38 x 2.0 =
        12.76  13 (2 sig figs)
                  Sig Dig Practice
   Calculation        Calculator says:     Answer
3.24 m x 7.0 m         22.68 m2            23 m2
100.0 g    23.7 cm3    4.219409283 g/cm3 4.22 g/cm3
0.02 cm x 2.371 cm 0.04742 cm2            0.05 cm2
710 m     3.0 s        236.6666667 m/s    240 m/s
1818.2 lb x 3.23 ft    5872.786 lb·ft     5870 lb·ft
1.030 g    2.87 mL     .358885 g/mL      .359 g/mL
     Rules for Significant Digits in
       Mathematical Operations
      Addition and Subtraction: The
    number of decimal places in the result
    equals the number of decimal places in
    the least precise measurement. Least
    places to the right of the decimal.

           6.8 + 11.934 =
      18.734  18.7 (3 sig figs)
     Rules for Significant Digits in
       Mathematical Operations
      Addition and Subtraction: The
    number of decimal places in the result
    equals the number of decimal places in
    the least precise measurement.

           6.8 + 11.934 =
      18.734  18.7 (3 sig figs)
                 Sig Dig Practice
   Calculation        Calculator says:   Answer
3.24 m + 7.0 m           10.24 m         10.2 m
100.0 g - 23.73 g         76.27 g        76.3 g
0.02 cm + 2.371 cm        2.391 cm       2.39 cm
713.1 L - 3.872 L         709.228 L      709.2 L
1818.2 lb + 3.37 lb       1821.57 lb     1821.6 lb
2.030 mL - 1.870 mL       0.16 mL        0.160 mL
         Nature of a Measurement

    Measurement – quantitative (quantity)
    observation consisting of 2 parts

      Part 1 - number

      Part 2 - scale (unit)


    Examples:
                   20 grams
          6.63 x 10-34 Joule x seconds
         The Fundamental SI Units
(le Système International, SI) Pg 34 Text


  Physical Quantity      Name      Abbreviation
  Mass                  kilogram       kg
  Length                 meter          m
  Time                  second          s
  Temperature            Kelvin         K
  Electric Current      Ampere          A
  Amount of Substance    mole          mol
  Luminous Intensity    candela         cd
SI Units
      Derived Quantity-Unit Pg 36
   A combination of Quantities and SI base units
            Example: Density = m/v

         Area = L x W       units 2 (squared)
          Volume – L x W x H units 3 (cubed)
           Volumetric Cube

1 ml = 1 cc = 1cm3   10 cm x 10cm x 10cm
                         1000cm3 = 1L
        Density = mass /volume
   What type of proportion is density?

   Example Calculations Page 40:
             Direct Proportion
   Direct Proportion Graph
   K (constant) = B / A
            Inverse Proportion
   Inverse (Indirect) Proportion Graph
   K (constant) = x y
        SI Prefixes common to Chemistry Pg 35

Prefix         Unit Abbr.    Exponent    What does it
                                           mean?


Mega               M           10 6     One million times
                                            greater
 Kilo              k           103       One thousand
                                         times greater
Hecto              h           10 2      One hundred
                                         times greater
Deka              da           10-1        Ten times
                                            smaller
Centi              c           10-2      One Hundred
                                         times smaller
Milli              m           10-3      One thousand
                                         times smaller
Micro                         10-6     One million times
                                            smaller
             Dimensional Analysis
   Dim. Analysis is a skill used to convert units.
   Dim. Analysis will use conversion factors = fractions
    equal to 1 of the same.
   Example of conversion factors
     12 eggs      or    1dozen
     1 dozen             12 eggs
   Conversion question:
    How many eggs are in 12.5 dozen?
   Solution: ? = given
               ? eggs = 12.5 dozen x 12 eggs
                                        1 dozen
Dimensional analysis with metric

          Practice writing conversion factors.
   Write two conversion factors for each of the following:
m and cm                m and km             m and mm
           Answers
m and cm    m and km    m and mm

1m         1 km         1 m___
100 cm     1000 m      1000 mm
 or          or           or

100 cm     1000 m      1000 mm
 1m          1 km          1m
                    Practice
   How many kg are in 10.5 g?
                 Solution
? kg = 10.5 g x 1 kg__ = .0105 kg
                1000 g
                Percent Error
   Percent Error = Actual – Theoretical x 100
                        Theoretical

OR
                = Experimental – Accepted x 100
                          Accepted
                 Types of Error
       Random Error (Indeterminate Error) -
    measurement has an equal probability of being
    high or low.

    Systematic Error (Determinate Error) - Occurs
    in the same direction each time (high or low),
    often resulting from poor technique or incorrect
    calibration.
    Steps in the Scientific Method
 1. Observations
   -   quantitative
   -   qualitative
   - what is the difference?
2. Formulating hypotheses
   -   possible explanation for the observation
3. Performing experiments
   -   gathering new information to decide
       whether the hypothesis is valid
    Outcomes Over the Long-Term
   Theory (Model)
    -  A set of tested hypotheses that give an
       overall explanation of some natural
       phenomenon.
   Natural Law
    -  The same observation applies to many
       different systems
   -  Example - Law of Conservation of Mass
              Law vs. Theory

     A law summarizes what happens
     A theory (model) is an attempt to
    explain why it happens.

								
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