Transcript Sig. Fig. Slides

Chapter 3: Measurement, Scientific
Notation, Significant
Figures
Sections 3.1-3.5
Chemistry 111
1
Topics
• Scientific Notation, Calculator
• Dimensional Analysis, Metric Prefixes, Per,
Cancelling, Unit Paths
• Exercise #1
• Recap / Go over Exercise
• Sig. Figs.
• Redo Ex #1, Fix sig. figs.
2
Scientific Notation
• Use
• Definitions
• Using the Calculator
3
Scientific Notation - Use
• Used to avoid:
602200000000000000000000
(or is it: 6022000000000000000000000?)
• And:
0.0000007
0.0000000000000000001609
0.000000000000000000000000000000000626
4
Scientific Notation: Definitions
• We split the number into a “coefficient” and “exponent”:
6.626 × 10-34
• Coefficient:
– A number between 1.0000 & 9.9999
– May be positive or negative
– Easy for sig. figs.!
• Exponent:
– A positive or negative whole number
– Corresponds to the number of decimal shifts.
– Not involved with sig. figs.
5
Scientific Notation: Calculator
• Why talk about it?
– Because you need to use the calculator
correctly.
– The calculator has a built-in function (EE or
EXP) button that helps you enter exponential
notation. If you learn it, it is easier, faster, more
correct. (& required for Chem111)
6
Scientific Notation: Calculator II
• Find your button:
EE
or
EXP
– Might require Shift or 2nd function key.
• Find your “Negative” Key (-) or +/• Follow Table 3.1: (3.96×104)(5.19 ×10-7)
• 3 . 9 6 EE 4 ×
x 5 . 1 9 EE +/- 7 =
• Notice that you don’t type ×10 ever, EE takes care of it.
• Do this & Master it today:
– There are ways to do it w/o the EE
EE button but I’ve got
tricky problems to trip you up.
7
Scientific Notation: Calculator III
• Try the ones in the book on page 51.
8
Dimensional Analysis
• Scientific Measurements
– Include the numerical value:
62.4
– Must also include the units:
mi/hr
– Number is written so it indicates how carefully
it was measured (3 s.f.) but let’s put this off
until later.
9
Dimensional Analysis (2)
• Converting between Units
– How fast is a Canadian going if his
speedometer says 62.4?
– How far does he move every 1 second?
10
Chapter 3 - Exercise #1
1. How many m are there in 2 miles?
a. miles  km  m  m
b. miles  ft  in  cm  m  m
2. The volume of a spherical Styrofoam ball with a diameter
of 40 mm is calculated by V=4/3××r3
a.
b.
c.
d.
e.
What is the volume? What are its units?
What is the volume in mL?
Draw a unit path from (b) to quarts.
What is the volume in Quarts?
What is the volume of 5 spherical balls in quarts?
Sig. Figs.: Ignore sig. figs. as you do this exercise – make it as ugly as you can!
Show your work: Write it out as if you’re teaching it to someone.!
11
Counting Significant Figures
1. Nonzero Integers. Nonzero integers always count as
significant figures.
2. Zeros. There are three classes of zeros:
1. Leading Zeros are zeros that precede all the nonzero digits.
These do not count as significant figures. In the number 0.0056,
the three zeros simply indicate the position of the decimal point.
This number has only two significant figures.
2. Captive Zeros are zeros between nonzero digits, these always
count as significant figures. The number 5.009 has four
significant figures.
3. Trailing Zeros are zeros at the right end of the number. They are
significant only if the number contains a decimal point.
12
Counting Significant Figures
Note 1: In Scientific notation, all digits in
the coefficient are significant
figures.
Note 2: Exact numbers can be considered to
have a  (infinite) number of
significant figures.
13
Rules for Computations & Sig. Figs.
1.
For multiplication and division, the number of
significant figures in the result is the same as the number
with the least precise measurement used in the
calculation. For example:
5.667 × 4.1 = 24.234
2.
For addition and subtraction, the
result has the same number of
decimal places as the least precise
measurement used in the
calculation. Set the problem up
like 2nd grade math!

24
5.11
20.5
+ 2.812
28.422  28.4
14
Rules for Computations & Sig. Figs.
Note 1: For multiplication and division – the
sig. figures are counted.
Note 2: For addition and subtraction – the
decimal places are counted.
15
Chapter 3 - Exercise #2
• On a new Sheet of paper:
– Redo the problems in Exercise #1
– Follow the sig. fig. rules.
– Show the work again.
• Remember that some numbers came from
definitions
– 1 inch  2.54 cm, exactly
– Whole numbers
– These have infinite sig. figs. – ignore them when
applying sig. fig. rules.
16