C: 22 September 2011
Take Out Homework: W eek 3 #1-5
and Lab Report
 Objective: You will be able to:
 differentiate between accurate and
precise measurements
 determine the number of significant
figures in any value
 Do now: Calculate the mass of a pure
copper penny (density = 8.92 g/cm3) with
a volume of 0.20 cm3.

Agenda
Do now
II. Track objective mastery
III. Go over homework
IV. Accuracy vs. precision notes and examples
V.
Practice problems
VI. Significant figures rules and examples
VII. Clicker practice problems
Homework: Week 3 Homework #6-10: Fri.
I.
Track Objective Mastery
Objective 8 (Density) Exit Ticket
 Unit 1 Pretest B Objectives 5-12


Where have you improved most?!
Density Exit Ticket
II. b. Calculate the volume of a piece of gold
(density = 19.32 g/cm3) that has a mass of
5.00 grams.
Expectations

During notes and example problems:
silently write them into your notebook
 Raise your hand to ask questions or
make comments
Reading a graduated cylinder
Precision and Accuracy
precision: how close a series of
measurements are to each other.
 accuracy: how close a series of
measurements are to the actual or true
value.

Volume of a sample of water
(Actual volume: 5 mL)
a.
b.
c.
d.
2.0 mL, 2.1 mL, 1.9 mL
4.0 mL, 5.0 mL, 6.0 mL
1.2 mL, 5.5 mL, 10.6 mL
4.9 mL, 5.0 mL, 5.0 mL
Mass of copper cylinder (g)
Massing 1
Massing 2
Massing 3
Massing 4
Larissa
47.45
47.39
47.42
47.41
Loveng
47.95
47.91
47.89
47.93
Lorreno
47.13
47.94
46.83
47.47
Three students made multiple weighings of a copper
cylinder, each using a different balance. The correct
mass of the cylinder had previously been determined
to be 47.32 grams. Comment on the accuracy and
precision of each student’s measurements.

Comment on the accuracy and
precision of these basketball free-throw
shooters:
 a. 99 of 100 shots are made
 b. 99 of 100 shots hit the front of the
rim and bounce off
 c. 33 of 100 shots are made, the rest
miss.
SWBAT determine the precision and accuracy of data.
On Your Own
a.
b.
c.
How are accuracy and precision similar?
How are accuracy and precision
different?
Give an example of a data set that is very
precise but not accurate. (Hint: You’ll
have to write down the “real” answer,
too.)
Percent Error: a measurement of
how accurate your data are
your _ value  actual _ value
100
actual _ value
1.
2.
So, if the actual value is 5.0 grams, but
your average mass was 4.6 grams, what is
your percent error?
What if your average volume was 25.0
mL, but the actual value is 23.9?
An engineer was responsible for calculating
amount of water that overflowed from a
dam. He measured all of the water runoff
going into the reservoir (1.2 million cubic
feet per year), the rainfall (860 cubic feet per
year), and the capacity of the reservoir (3.8
million cubic feet). He did some fancy
calculations. He reported to his boss that the
overflow from the dam would be
350,246.2544330 cubic feet per year.
 What’s wrong here?

Significant Figures
How to determine how accurate a number
is
 How to determine how much to round an
answer

I. Significant Figures
aka: Significant Digits

A. Nonzero integers count as significant
figures
 Ex. Any number that is NOT zero (1, 2, 3,
4, 5, 6, 7, 8, 9)
 345
 597.2
 145.456
SWBAT identify and round a number to the correct number of significant figures.

Zeros
 B. Leading zeros that come before all
the nonzero digits do NOT count as
significant figures
 Ex: 0.0025 has two sig. fig. The zeros
are “leading” and do not count.
 0.23
 0.0004
 0.03564
SWBAT identify and round a number to the correct number of significant figures.
 C.
Captive zeros are between nonzero
digits and DO count as sig. fig.
 Ex: 1.008 has four sig. fig. The zeros are
captive and DO count.
 10,004
 1.000006
 1,000,000,000,000,567
SWBAT identify and round a number to the correct number of significant figures.



D. Trailing zeros are to the right end of
the number and DO count as sig. fig. if the
number contains a decimal point.
Ex.: 100 has only one sig. fig. because the
trailing zeros DO NOT have a decimal
point.
Example: 1.00 has three sig. fig. because
the trailing zeros DO have a decimal point.
SWBAT identify and round a number to the correct number of significant figures.
More practice: Trailing zeros






1.000000
3,000,000
3.00000
30.00
300
300.

E. Exact numbers
 Any number found by counting has an
infinite number of significant figures.
 Ex: I have 3 apples. The 3 has an
infinite number of significant figures.
 50 people
 100 baseballs
SWBAT identify and round a number to the correct number of significant figures.
Which are exact numbers?
1.
2.
3.
4.
5.
6.
The elevation of Breckenridge, Colorado
is 9600 feet.
There are 12 eggs in a dozen.
One yard is equal to 0.9144 meters.
The attendance at a football game was
52,806 people.
The budget deficit of the US government
in 1990 was $269 billion.
The beaker held 25.6 mL of water.
SWBAT identify and round a number to the correct number of significant figures.
Clicker Use
Always pick up and use only your assigned
clicker: You are responsible for it!
 Remain silent while the question is being
read and while you answer – only answer
for yourself!
 Never laugh at, mock or ridicule the
proportion of students answering
incorrectly.
 Listen carefully as the answer is explained.

How many significant figures?
256
1.
2.
3.
4.
1
2
3
4
95%
0%
1
5%
0%
2
3
SWBAT identify and round a number to the correct number of significant figures.
4
How many significant figures?
647.9
1.
2.
3.
4.
1
2
3
4
95%
5%
1
0%
2
0%
3
SWBAT identify and round a number to the correct number of significant figures.
4
How many significant figures?
647.0
1.
2.
3.
4.
1
2
3
4
73%
27%
0%
1
0%
2
3
SWBAT identify and round a number to the correct number of significant figures.
4
How many significant figures?
321.00
1.
2.
3.
4.
2
3
4
5
94%
6%
1
0%
2
0%
3
SWBAT identify and round a number to the correct number of significant figures.
4
How many significant figures?
4005
1.
2.
3.
4.
1
2
3
4
86%
14%
0%
1
0%
2
3
SWBAT identify and round a number to the correct number of significant figures.
4
How many significant figures?
nine
1.
2.
3.
4.
1
2
3
infinite
67%
33%
0%
1
2
0%
3
SWBAT identify and round a number to the correct number of significant figures.
4
How many significant figures?
200.
1.
2.
3.
4.
1
2
3
4
82%
14%
5%
1
0%
2
3
SWBAT identify and round a number to the correct number of significant figures.
4
How many significant figures?
200.0
1.
2.
3.
4.
1
2
3
4
100%
0%
1
0%
2
0%
3
SWBAT identify and round a number to the correct number of significant figures.
4
How many significant figures?
0.009009
1.
2.
3.
4.
2
4
6
7
58%
42%
0%
1
0%
2
3
SWBAT identify and round a number to the correct number of significant figures.
4
How many significant figures?
-500
1.
2.
3.
4.
1
2
3
4
57%
43%
0%
1
2
0%
3
SWBAT identify and round a number to the correct number of significant figures.
4
How many significant figures?
-500.
1.
2.
3.
4.
1
2
3
4
100%
0%
1
0%
2
0%
3
SWBAT identify and round a number to the correct number of significant figures.
4
How many significant figures?
1.3x1032
1.
2.
3.
4.
1
2
3
4
SWBAT identify and round a number to the correct number of significant figures.
How many significant figures?
1.
2.
3.
4.
A student’s extraction procedure yields
0.0105 g of caffeine.
A chemist records a mass of 0.050080 g
in an analysis.
In an experiment, a span of time is
determined to be 8.050 x 10-3 s.
Rewrite 8.050 x 10-3 so it has three
significant figures.
SWBAT identify and round a number to the correct number of significant figures.
Assignment
In your lab notebook, find the density
stations from yesterday.
 Next to each value you measured, write
the number of significant figures in a
circle.
 Ex: 12.35 cm 4

Exit Ticket
Homework

Week 3 Homework #6-10: Fri.
C: 23 September 2011
Rounding
Take Out Homework: Week 3 Homework #1-10
 Objective: You will be able to:
 round values to the correct number of
significant figures
 Do now: How many significant figures?
 a. 0.00045
 b. 0.00040
 c. 0.0004050
Agenda
Do now
II. Go over homework
III. Accuracy/Precision, Sig. Fig. “Exit” Ticket
IV. Rounding Notes and Examples
V.
Practice Problems
VI. Exit Ticket
Homework: Week 3 Homework #11-14: Mon.
I.
“Exit” Ticket
Precision/Accuracy
 Sig. Fig.

Rounding
The answer to a calculation can not be
any more accurate than the least accurate
value in that calculation.
 When multiplying or dividing, round to
the least number of significant figures
given in the problem.

Example 1

An iron block with side lengths 10.5 cm by
22.6 cm by 2.5 cm has a mass of 4655
grams. Calculate the density of iron.
Example 2

The density of mercury is 13.53 g/cm3.
Calculate the volume taken up by 5.0
grams of mercury.
Problems
1.
2.
Calculate the mass of a cube of silver with
side length 5.0 cm. Silver has a density
of 10.49 g/cm3.
Calculate the density of a stack of gold
coins with mass 1100 grams and volume
of 51.76 cm3.
Exit Ticket

Rounding
Homework

Week 3 Homework #11-14: Monday
C: 28 September 2011
Objective: You will be able to:
 round a calculation to the correct
number of sig. fig.
 plan a procedure and data table for a lab
on the density of pennies
 Do now: Round to TWO sig. fig:
a. 0.003563725
b. 5,723

Agenda
Do now
II. Tracking Objectives – Rounding
III. Rounding Worksheet
IV. Pennies lab: Plan procedure
V. Design a data table
Homework: Quiz Friday: Objectives 8-11
I.
Tracking Objectives

Rounding Exit Ticket: Objective 11
Rounding Practice (10 min.)
Quietly, on your own
 If you have a question, you may consult
your partner or raise your hand to ask me
a question.
 When you are done, have me check your
work.
 Then, complete the exit ticket on your
own.

With your lab group (20 min.)
In your notebook:
 Copy the research questions
 Make two hypotheses (one for each
research question)
 On the poster paper as a group:
 Write your complete and detailed
procedure

Gallery Walk (8 min.)
With a marker, read another group’s
procedure.
 Make constructive comments in writing
 “How big is the graduated cylinder?”
 “I like how you were specific about what
to change in each trial!”
 Then, visit another group’s poster and do
the same thing.

Together:

Construct the procedure we will all follow
from the best elements of everyone’s
group posters.
As a lab group

Design your data table for next class!
Homework
Quiz Friday: Objectives 8-11
 Finish Procedure

A: 27 September 2011
Objective: You will be able to:
 determine the relationship between
mass and volume of pennies.
 compare the density of pre- and post1982 pennies.
 Do now: Round to THREE sig. fig:
a. 0.003549248
b. 356,908,256

Agenda
Do now
II. Tracking Objectives
III. Carry out your procedure and collect data!
IV. Finish calculations
Homework: Finish Unit 1 Pretest B:
tomorrow
Be sure all your density calculations are done.
Objectives 8 through 11 quiz tomorrow
I.
Track Quiz and Exit Ticket

Did you get less than a 3 or 4 on
Objectives 1 through 4?
 Come for extra help after school!
 Re-take a quiz on that objective after
school or next time we have a quiz.
 Your goal is to earn a 3 or a 4 for EVERY
objective!!
Carry out your procedure
Split up the work to be most efficient.
 Work carefully.
 Estimate the last digit on the graduated
cylinder.
 Neatly record your data in a table in your
notebook.
 Make sure your station looks as neat when
you are finished as it did when you started!

Equipment
250 mL beaker
 vinegar
 100 mL graduated cylinder
 electronic balance
 water

Homework
Be sure all your density calculations are
done.
Objectives 8-11 Quiz Thursday (study exit
tickets!)
We’ll finish this lab tomorrow!
C: 30 September 2011
Objective: You will be able to:
 show what you know about objectives 811.
 Do now:
 Look at your tracking sheet Quiz grades
for objectives 1-4. Write down the
number of any objectives you have not
yet earned a 3 or 4 on.

Agenda
Do now
II. Track Rounding (Obj. 11) exit ticket 2
III. Objectives 8-11 Quiz!
IV. Make up Objectives 1-4 Quizzes
V.
Work on lab graph, analysis and conclusion
Homework: Week 4 Homework p. 1: Mon.
Lab graph, analysis and conclusion: due
Monday
I.
Properties
Intensive: the property does NOT depend
on the amount of stuff you have
 ex: temperature
 Extensive: the property DOES depend on
the amount of stuff you have
 ex: mass
 Use your data to determine if density is an
intensive property or an extensive
property!

Track Rounding (Obj. 11)

You can erase/cross out your first exit
ticket score if you earned a higher score!
When you finish your quiz…
Raise your hand and tell me if you need to
retake any objective 1-4 quizzes.
 Once you are done with quizzes, work on
graphing your data, writing an analysis and
conclusion
 Look at the lab handout for all the details!
 Work on this silently until everyone is
done with their quizzes.

Need help on the lab?
Need extra help before you retake a quiz?
 Work with me after school Monday!

Homework
Lab notebook: Monday
 Week 4 Homework p. 1: Mon.

C: 29 September 2011
Homework: Density of Pennies
Procedure
 Objective: You will be able to:
 determine the relationship between mass
and volume of pennies and compare
density
 Convert between scientific and regular
notation.
 Do now: Read through your procedure.
Write down one question you have about it
to share with your lab group.

Agenda
Do now
II. Carry out your procedure and collect data!
III. Finish calculations and graph data
IV. Graph Data
V.
Scientific notation notes and practice
Homework: Week 4 Homework page 1:
Mon.
Pennies lab analysis and conclusion: Monday
Objectives 8 through 11 quiz tomorrow
I.
By 9:15…
Collect your data and organize it into the
nicest table you have ever made
 See the lab handout for more details.
2. Graph both data sets on one set of axes –
this should be the nicest graph you have
ever made
 See the lab handout for more details.
 Complete the analysis and conclusion in
your lab notebook.
1.
Scientific Notation
Homework
Pennies lab analysis and conclusion: Friday
Objectives 8 through 11 quiz
tomorrow

The sample of gold contained
1,200,000,000,000,000,000,000,000,00
0 atoms.
How do we keep track of ALL those zeros?
 In chemistry, some numbers are HUGE!

III. Rules for Sig. Fig. in Mathematical
Operations

A. Multiplication and Division
 The number of sig. fig. in the results
should be the same as the number of sig.
fig. in the least precise measurement
used in the calculation.
 Example: 4.56 x 1.4 = 6.38  6.4

B. Addition and Subtraction
 The result should have the same number
of decimal places as the least precise
measurement used in the calculation.
 Example: 12.11 + 18.0 + 1.013 = 31.123
 31.1 (one decimal place)
13 x 1.000 = 13.000 =
 23.45 x 400 = 9380 =
 5000 / 3.12 = 1602.56410256…


14 + 3.567 = 17.567

56.2 + 23.988 = 80.188

100 – 1.9995 = 98.0005
IV. Rounding
Calculate first, then round
 Example: round 4.348 to two sig. fig.
 4.3
 Never round until your final answer!

Converting between SI units

notes from the board
SWBAT convert between units in the SI system.
SI Unit Prefixes
Steps to Conversions
1.
2.
3.
4.
5.
6.
7.
Identify and write your known and
unknown.
Choose an equality.
Make a fraction
Put units to cancel on the bottom
Put units to remain on the top
Cancel units and compute
Report answer with units!
Practice Problems
1 liter = 1000 milliliters
1. How many liters are equal to 550
milliliters?
2. How many milliliters are equal to 3.5
liters?
3. How many liters are equal to 45,000
milliliters?
4. How many milliliters are equal to 354
liters?

SWBAT convert between units in the SI system.
1 meter = 100 cm, 1 kilometer = 1000 meters
1. How many meters are equal to 500
centimeters?
2. How many centimeters are equal to 850
meters?
3. How many meters are equal to 37.5
kilometers?
4. How many centimeters are equal to 5.8
kilometers?

SWBAT convert between units in the SI system.