significant figures

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CHEMISTRY
July 31, 2012
Brain Teaser (write the question &
answer)
 Convert 100m to cm.
 Convert 158 kL to L.
 Convert 85 mg to kg.
 How many sig digits are in 0.0031324?
 How many sig digits are in 12.40?
 How many sig digits are in 386.042?
 How many sig digits are in 3100.0 x 10^2?
Introduction to Chemistry
 Chemistry: The
 Chemistry is the science
Central Science
that investigates and
explains the structure and
properties of matter.
 Seeks to explain the
submicroscopic events
that lead to macroscopic
observations
Branches of Chemistry
Branch
Area of Emphasis
Examples
Organic
chemistry
most carbon-containing chemicals
pharmaceuticals,
plastics
Inorganic
chemistry
in general, matter that does not
contain carbon
minerals, metals and
nonmetals, semiconductors
Physical
chemistry
the behavior and changes of matter
and the related energy changes
reaction rates,
reaction mechanisms
Analytical
chemistry
components and composition of
substances
food nutrients, quality
control
Biochemistry
matter and processes of living
organisms
metabolism,
fermentation
Units of measurement
SI Units (Le Systéme Internationale)
 Scientists need to report data that can be
reproduced by other scientists. They need
standard units of measurement.
Base Units
• A base unit is a defined unit in a system of
measurement
•There are seven base units in SI.
Base Units
Why do we use the (SI) system?
 Advantages
Simple to use
 Easy to convert from one unit to another



Dimensional Analysis
Universal – used worldwide


By all scientists to communicate
By all industrialized nations
 Except United States
 U.S. loses billions of dollars in trade
Practice
 Convert 10mL to KL
 Convert 5.3g to cg
Accuracy and Precision
Data Terms
 Quantitative
Measurements
Give results in a definite
form, usually values
 Examples
24L, 10 cm, 14 ºC
Data Terms
 Qualitative
Measurements
 Examples
Give results in a descriptive,
non-numeric form.
The beaker was warm.
The density was greater
than that of water.
Data Terms
 Accuracy
 Examples
How close a measurement
comes to the actual value of
whatever is being measured
Water freezes at 0º C, and
boils at 100º C. How close
is the measurement to the
values.
Data Terms
 Precision
Reproducibility of the
measurement
 Examples
9 out of 10 lab groups report the
temperature of boiling water to
be 95º C.
A basketball player shoots 20
free throws, 18 of which
bounce off the right side of the
rim.
Accuracy vs. Precision
 Target Practice
 Accurate
Precise
Accurate
&
Precise
An archery target illustrates the difference between accuracy and precision.
Accuracy and Precision
Measurements
Scale Reading and Uncertainty
 Uncertainty: Limit of precision of the reading
(based on ability to guess the final digit).

Existed in measured quantities versus counted quantities
Percent error
Theoretical – Experimental x 100 = % error
Theoretical
SIGNIFICANT
FIGURES
Significant Figures
 Significant
Figures
Digits in a measurement that
have meaning relative to the
equipment being used
Significant Figures
 Place
What is the increment on the
equipment?
What you know for sure.
Significant Figures
 Digits with
meaning
Digits that can be known
precisely plus a last digit that
must be estimated.
Triple Beam Balance (DO NOT USE)
 http://www.wisc-
online.com/objects/index_tj.asp?objID=GCH2
02
 DO NOT USE
 What are the units?
Ruler
 http://www.funbrain.com/measure/
 What are the units?
Graduated Cylinder
 http://www.uwplatt.edu/chemep/chem/chemsc
ape/labdocs/catofp/measurea/volume/gradcyl
/gradcyl.htm
 What are the units?
Significant Figures
 What do you
notice?
Depends on type of equipment
being used.
Depends on size of equipment
used.
Significant Figures
 Raw Data Rules

How do you
know how many
sig figs?
1. All digits 1-9 are significant.
2. Zeros between significant
digits are always significant.
3. Trailing 0’s are significant only
if the number contains a
decimal point
4. Zeros in the beginning of a
number with a decimal point
are not significant.
5. Zeros following a significant
number with a decimal are
significant.
Significant Figures
 Pacific to
Atlantic Rule
Pacific = Decimal Present
Start from the Pacific (left
hand side), every digit
beginning with the first 1-9
integer is significant
 Examples
20.0 = 3 sig digits
0.00320400 = 6 sig digits
1000. = 4 sig digits
Significant Figures
 Atlantic Rule to
Pacific
Atlantic = Decimal Absent
Start from the Atlantic (right
hand side), every digit
beginning with the first 1-9
integer is significant
 Examples
100020 = 5 sig digits
1000 = 1 sig digits
Practice

1.
2.
3.
4.
How many significant figures are in
400.0
4000
4004
0.004
Rally Rows
How many significant figures are in
1. 0.02
2. 0.020
3. 501
4. 501.0
5. 5000
6. 5000.
7. 5050
8. 01.0050
9. 50300
10. 5.0300
Review Questions
 Determine the number of significant figures
in the following:







1005000
1.005
0.000125
1000.
0.02002
2002
200.200
Review Questions
Determine the number of significant figures in:
 72.3 g
 60.5 g
 6.20 g
 0.0253 g
 4320 g
 0.00040230 g
 4.05 x 10^5 g
 4500. g
Quick Review
 What are
Significant
Digits?
 Examples
 Triple
Beam
Balance
 Graduated
Cylinder
 All the certain digits plus the
estimated digit in a
measurement.
 How many decimal places can
we count

Hundreths

Depends on the size
Significant Figures in Calculations
 Exact
 Do not affect the number of
Numbers
 Examples
 Infinite
sig figs
# of
significant digits in the final
answer. They are not
measurements!!
 1000m = 1 km
 12 in = 1 foot
Significant Figures in Calculations
 Multiplication
and Division
 Example
 The number with the
smallest number of
significant digits determines
how many significant digits
are allowed in the final
answer.
 Volume of a box
L x W x H
 (3.05m)(2.10m)(0.75m)
 2 sig figs
 4.8m3
Significant Figures in Calculations
 Example
 Density
D
of a
penny
 M = 2.53g
V = 0.3mL
=M/V
 # significant figures allowed
 D = 8g/mL
Significant Figures in Calculations
 Addition and
Subtraction
 Example
 The number of significant
digits depends on the number
with the largest uncertainty.
(you may be using different
scales)
Shoes
951.0 g
Clothes 1407
g
Ring
23.911 g
Glasses 158.18 g
Total
2540.
g
Significant Figures in Calculations
 Example
 What is the mass of a penny
if, the weighing paper alone
has a mass 0.67 g and
weighing paper plus the
penny has a mass of 3.2 g.
3.2 g
-0.67 g
2.5 g
Significant Figures in Calculations
 Remember
A calculated number can only
be as precise as the least
precise measurement in the
calculation.
Practice
Calculate each of the following to the correct
number of significant figures. Include units on
your answer.
1. (25 g/mol)(4.0 mol) =
2. (3.48 in)(1.28 in)(0.010 in) =
3. 2.06 cm + 1.8 cm + 0.004 cm =
4. If the mass of a lead cube is 176.91 g and it
measures 2.51cm x 2.49 cm x 2.49 cm, what
is the density of lead?
Practice
Calculate each of the following to the correct
number of significant figures. Include units on
your answer.
1. (25 g/mol)(4.0 mol) =1.0 x 102
2. (3.48 in)(1.28 in)(0.010 in) = .045 in3
3. 2.06 cm + 1.8 cm + 0.004 cm = 3.9 cm
4. If the mass of a lead cube is 176.91 g and it
measures 2.51cm x 2.49 cm x 2.49 cm, what is
the density of lead? 11.3 g/cm3
Rally rows
Sig figs in Calculations
1.
2.
3.
4.
5.
12 cm + 0.031cm + 7.969 cm =
(41.025 g - 23.38g) ÷ 8.01 mL=
17.3 cm x 6.2 cm + 3.28 cm2 =
109.3758 m2  45.813 m =
What is the mass of Salt (NaCl) if the
sodium has a mass of 22.99 g and the Cl a
mass of 35.5g?
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