# 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
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
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
 For non-electronic devices, an estimated place
value must be obtained from reading the
instrument.
The Thermometer
and Significant Digits.
o Determine the
the scale on the
thermometer at eye
level.
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
Use the graduations to find all certain
digits

There are two
below the meniscus,
represents 1 mL, so
the certain digits of
Estimate the uncertain digit and take a

eight tenths of the
way to the next
final digit in the

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

6 6 2
_ . _ _ mL
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
_ _ _
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:
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
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
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
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
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
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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