•Metric System
•Prefixes
•Conversions
•Scientific Notation
•Writing
•Calculating
•Significant Figures
•Definition
•Counting
•Calculating
•Dimensional Analysis
• AKA: International
System (SI)
• 1960: international
agreement set up to
use this system of
units
• Our “English system”
is used within our
boundaries, but we
use the metric system
in international trade.
• 1999: NASA $125
million dollar mistake
• Graphic organizer for prefixes
– Mnemonic device: The good man King Henry
died by drinking chocolate milk Monday night,
poor fellow.
– Prefixes
– Powers of Ten
– Place holders
Oops!
– Conversions
• Temperature
– Kelvin & Celsius
As you come in,
The Materials:
1. Put any email slips on the front desk.
2. Tarvin Consulting Group supplies
3. Pen/pencil and paper for a few notes
The Plan:
1. Any questions about Element Quiz scheduled for Friday?
2. Work on Tarvin Consulting Group activity. (30 min)
3. Review the metric system. Solve and check 1-4 Practice
Problems.
4. Begin Introductory Metric System Lab.
5. Discuss scientific notation. (POSSIBLE)
The Practice:
In your practice packet: Any metric system practice & review
examples
The Assessment:
METRIC SYSTEM QUIZ TOMORROW!
Element Quiz on Friday!
Sample Element Quiz
Questions
1.
2.
3.
4.
5.
6.
Co _______________________
Cr ________________________
Sn _______________________
Copper ____________________
Sodium ____________________
Iron ________________________
Moving the Decimal
T // G // M // k h D base d c m // µ // n // p // f
1-4 PP#1
Convert 83 cm into meters.
T // G // M // k h D base d c m // µ // n // p // f
0.83 meters
1-4 PP #2
Convert 459 L into milliliters.
T // G // M // k h D base d c m // µ // n // p // f
459,000 mL
1-4 PP #3
Express 1123 pg in nanograms.
T // G // M // k h D base d c m // µ // n // p // f
1.123 ng
1-4 PP #4
Express 0.032 m3 in liters.
TRICKY!
1 cm3 = 1 mL
Steps:
1. Convert 0.032 m3 to cm3.
This equals mL.
2. Convert mL to L.
TRY IT.
HOW TO CONVERT 0.032m3 to L
1. Convert 0.032 m3 to cm3.
a) Cubed conversions are different from simple meter to
centimeter conversions.
b) Move the decimal 2 spaces to the right to go from
meter to centimeter, correct? NOT SO FAST!
c) Move the decimal 2 spaces for EACH dimension.
Since the unit is cubed, we’ll move the decimal 2
spaces to the right X 3!
d) 0.032 m3 = 32,000 cm3
2. Convert mL to L.
a) Since cm3 = mL, 32,000cm3 = 32,000 mL.
b) Move the decimal 3 spaces to the left to go from milli
to liters.
c) 32,000 mL = 32 L
1-4 PP #5
Express 2.5 mm in micrometers.
T // G // M // k h D base d c m // µ // n // p // f
2,500 micrometers
1-4 PP #6
Which is the longer amount of
time: 1351 ps or 1.2 ns?
A.) 1351 ps
B.) 1.2 ns
T // G // M // k h D base d c m // µ // n // p // f
1351 ps
1-4 PP #7
Which is the larger pressure:
232.1 kPa or 125,487 Pa?
A.) 232.1 kPa
B.) 125,487 Pa
T // G // M // k h D base d c m // µ // n // p // f
232.1 kPa
1-4 PP #8
Which is the smaller mass: 285.0
cg or 23.78 dg?
A.) 285.0 cg
B.) 23.78 dg
T // G // M // k h D base d c m // µ // n // p // f
23.78 dg
1-4 PP #9
Which is shorter: 175.6 mm or
38.4 cm?
A.) 175.6 mm
B.) 38.4 cm
T // G // M // k h D base d c m // µ // n // p // f
175.6 mm
1-4 PP #10a
0.7824 mg to grams
T // G // M // k h D base d c m // µ // n // p // f
0.000 782 4 grams
1-4 PP #10b
345,000 ng to grams
T // G // M // k h D base d c m // µ // n // p // f
0.000 345 000 grams
1-4 PP #10c
0.00378 kg to grams
T // G // M // k h D base d c m // µ // n // p // f
3.78 grams
1-4 PP #10d
34,981 micrograms to grams
T // G // M // k h D base d c m // µ // n // p // f
0.034 981 grams
•Lazy way to report
really BIG or small
numbers
•Uses powers of ten
rather than long
strings of zeros
•+ powers mean
BIG numbers
•- powers mean
small numbers
Expand or contract.
1. 250 = ______________
2. 13,210,000 = ________
3. 0.00150 = ___________
4. 14 = ________________
5. 0.00005 = ____________
6. 1.6x10-4 = ____________
7. 2.15x105 = ____________
8. 1.0x101 = _____________
9. 4.3x10-2 = ____________
Check your answers.
1. 250 = 2.5 x 102
2. 13,210,000 = 1.321 x 107
3. 0.00150 = 1.5 x 10-3
4. 14 = 1.4 x 101
5. 0.00005 = 5 x 10-5
6. 1.6x10-4 = 0.00016
7. 2.15x105 = 215,000
8. 1.0x101 = 10
9. 4.3x10-2 = 0.043
•Use the EE or EXP button to enter scientific notation.
•NEVER use the ^ or x10.
•Example:
•Enter 6.02 x 1023 into your calculator.
•Punch 6.02 as normal.
•Then push the EE or EXP button. It replaces the
x10.
•Lastly, enter 23.
•Summary: 6.02 EXP 23
1.
2.
3.
4.
6.02x1023 x 18.998 = ____________
5.6x10-8 / 3.2x10-3 = _____________
2.5x101 + 3.5x102 = _____________
8.45x10-3 x 2.1x101 = ____________
1. 1.144x1025 2. 1.75x10-5
3. 375
4. 0.17745
•
Density is used to identify substances
found in nature.
•
Density = mass/volume
•
Common units: g/mL or g/cm3
–
–
mL measures the volume of a liquid. It is
NOT a cubed unit.
cm3 measures the volume of a solid where
length, width, and height were multiplied
together.
Example of Density:
A rectangular sample is found.
What is the density?
1. Measure the mass with a balance.
2. Measure the volume with a ruler
since it has a normal (regular) shape.
3. Calculate.
Another Example of Density:
A strangely shaped sample is found.
What is the density?
1. Measure the mass with a balance.
2. Measure the volume with a
graduated cylinder using the water
displacement method.
3. Calculate.
A truth about the density of water:
• A 1 cm3 box will hold EXACTLY 1 mL of
water, and the 1 mL of water will weigh
EXACTLY 1 gram!
• Therefore, 1 cm3 = 1 mL = 1 gram.
• You are going to have a chance to prove
this in your lab today using a small blue
solid (not hollow) cube.
Density of a Metal Cube Lab
Goals: Test the 1 mL = 1 cm3 rule and determine
the type of metal that makes up your group’s
cube using density.
Steps: Follow the lab steps carefully, and be
sure to record any measurements on your
paper. You’ll have a very small lab report due
on Monday. The specifics of the report are
described on your lab handout. If you get
stuck, send a group rep to Mrs. Tarvin.
NOTE: The copy of the lab at your station should
not leave the station. A copy of the lab is on
the blog for your use at home.
A student determines that a piece of an
unknown material has a mass of 5.854 g
and a volume of 7.57 cm3. What is the
density of the material?
(Density Practice Problems #1)
A.) 0.773 g/cm3
B.) 1.29 g/cm3
C.) 44.4 g/cm3
D.) none of these
A student determines that a piece of an
unknown material has a mass of 5.854 g
and a volume of 7.57 cm3. What is the
density of the material?
(Density Practice Problems #1)
Steps:
1. Density = mass / volume
2. Mass = 5.854 grams; Volume = 7.57 cm3
3. Notice that the units will be grams/cm3. The
problem doesn’t specify certain units, so I can
use these.
4. 5.854 gram/7.57 cm3 = 0.773 g/cm3
Iron has a known density of 7.87 g/cm3.
What would be the mass of a 2.5 dm3 piece
of iron?
Density Practice Problem #2
A.) 1.9675 grams
B.) 19.675 grams
C.) 196.75 grams
D.) 19, 675 grams
Iron has a known density of 7.87 g/cm3.
What would be the mass of a 2.5 dm3 piece
of iron?
Density Practice Problem #2
Steps:
1. Density = mass / volume
2. Density = 7.87 g/cm3; Since the units are given for
density, I am stuck with them. I cannot plug in a mass
unless it is in grams. I cannot plug in a volume unless
it is in cm3.
3. Convert 2.5 dm3 to cm3. Move the decimal to the right
THREE spaces.
4. 7.87g/cm3 = mass / 2500 cm3 ; mass = 19,675 grams
Mercury has a density of 13.5 g/cm3.
How much space (in mm3) would
50.0 g of mercury occupy?
Density Practice Problem #3
A.) 3.70 mm3
B.) 37.0 mm3
C.) 370.0 mm3
D.) 3,700 mm3
Mercury has a density of 13.5 g/cm3. How
much space (in mm3) would 50.0 g of mercury
occupy?
Density Practice Problem #3
Steps:
1. Density = mass / volume
2. Density = 13.5 g/cm3; The mass MUST be in grams, and the
volume MUST be in cm3.
3. 13.5 g/cm3 = 50.0 g / volume; REMEMBER – The volume will be
in cm3 because of the density units.
4. ALGEBRA HELPFUL HINT: Put a 1 under the density & cross
multiply.
5. 13.5 g/cm3 = 50.0 grams
1
volume
(13.5 g/cm3)(volume) = (50.0 grams)(1)
(13.5 g/cm3)
(13.5 g/cm3)
volume = 3.70 cm3 = 3,700 mm3
A sample has a mass of 1.02g and
3
a volume of 1.35cm , what is the
density of the nickel?
Density Practice Problems #4
A.) 0.756 g/cm3
B.) 1.38 g/cm3
C.) 1.32 g/cm3
D.) 7.56 g/cm3
What is the density of a material if
its mass 2.02g and its volume is
0.500cm3?
Density Practice Problem #5
A.) 1.01 g/cm3
B.) 4.04 g/cm3
C.) 0.248 g/cm3
D.) 4.48 g/cm3
Pure gold has a density of 19.32
g/cm3. How large (in dm3) would a
piece of gold be if it had a mass of
318.97 g?
Density Practice Problems #6
A.) 16.51 dm3
B.) 1.651 dm3
C.) 0.1651 dm3
D.) 0.01651 dm3
How many cm3 would a 55.932 g
sample of copper occupy if it has a
density of 8.92 g/cm3?
Density Practice Problems #7
A.) 0.159 cm3
B.) 499 cm3
C.) 6.27 cm3
D.) 48.9 cm3
hey mrs tarvin,
im sitting in my awesome chem lecture hall
and we're doing review. i was wondering if
you could remind me of what your sigfig tricks
were to remember when to count them and
when not to.
thanks!
alexandra
ps, i hope you've got some great classes!
I got this email yesterday during 4th pd from UGA
Digits in measurement communicate valuable quantitative
information. If you know your stuff, the digits can tell you
qualitative information, too.
Example:
Compare the information in these two numbers. Don’t
forget to read between the lines!
a. 148,300 meters
b. 148,336.420 meters
Making Measurements
1. Examine the markings on the instrument. Note the
smallest mark shown and the unit that you’ll be using.
What decimal place does the smallest mark represent?
2. Measure the object as usual, and record all of the
obvious markings.
3. THEN, ADD ONE ADDITIONAL DECIMAL PLACE TO
YOUR MEASUREMENT. (ONE PAST THE MARKINGS
OF THE INSTRUMENT.)
Making Measurements
1. The ruler is marked to the nearest 1/10 of a centimeter.
In other words, the smallest marking is 0.1 cm.
2. The object measures EXACTLY 5.7 cm according to the
obvious markings.
3. In science, we record the one estimated digit beyond the
obvious markings. We should record the measurement
as 5.70 cm. (Note: Answer has ONE extra decimal
place beyond the smallest marking.)
Making Measurements
What if you disagree with my estimate? What if
you believe that the object is not EXACTLY on
the 5.7 mark?
Then, you would use a different estimated
digit.
Examples:
5.72 cm or 5.75 cm or 5.79 cm
Analyzing measurement data:
•Describing the instrument
•Evaluating the “worth”
Example:
Consider the data recorded below.
Length: 3.50 cm
Width: 2.150 cm
Could these have been made by the same instrument? How
sensitive is the instrument?
Some instruments are better than others,
and we may all estimate different final
digits in our measurements. Error is an
important consideration in our
measurements and calculations then.
CONSIDER: What if you were asked to calculate the
volume of a block? Volume includes THREE
measurements (L x W x H). You could have THREE
small errors factoring into your volume answer.
Special rules exist in scientific calculations to prevent
error from “snowballing” in our answers.
Remember, measurements involve estimations, and that
can be dangerous when working with volatile chemicals.
Reducing the estimation risk:
•When adding or subtracting:
•Line up the decimals as usual.
•Draw a vertical line at the end of the shortest #.
•Add or subtract. Round the answer at the line.
Addition and Subtraction Example
35.6 + 4.1 + 4.79 + 2 =
Step 1: Line up the decimals.
35.6
4.1
4.79
+2
Step 2: Draw a vertical line at
the end of the shortest #.
35.6
4.1
4.79
+2
Step 3: Add & round at the line.
46.49 = 46
1. 61.2 meters + 9.35 meters + 8.6 meters
2. 9.44 meters - 2.11 meters
3. 34.61 meters -17.3 meters
4. 8.3 meters x 2.22 meters
5. 8432 meters /12.5
1. 79.2 meters
2. 7.33 meters
4. 18 meters
5. 675 meters
3. 17.3 meters
Reducing the estimation risk:
•When multiplying or dividing:
•Count the significant digits in all #’s.
•Multiply or divide. Round the answer to the smallest number of sig figs.
Learning to Count Sig Figs:
Imagine the number inside the US.
• Imagine the number inside the
US.
• If the decimal is PRESENT, go to
the Pacific coast of the #. Look
back across the # and begin
counting digits at the 1st nonzero
#. Don’t stop counting until you
run out of digits no matter what!
EXAMPLE: How many sig figs are in 0.0780400?
P
0.0780400
123456
6 sig figs!
A
• Imagine the number inside the
US.
• If the decimal is ABSENT, go to
the Atlantic coast of the #. Look
back across the # and begin
counting digits at the 1st nonzero
#. Don’t stop counting until you
run out of digits no matter what!
EXAMPLE: How many sig figs are in 56,043,000?
P
56,043,000
54321
5 sig figs!
A
Counting sig figs:
1. 0.05730 meter
2. 8765 meters
3. 0.00073 meters
4. 40.007 meters
5. 143 grams
6. 8.750x10-2 grams
7. 1.40x10-5 grams
1. 8.3 meters x 2.22 meters
2. 8432 meters /12.5
1. 18 meters
2. 675 meters
Density Practice Problems
1.
2.
3.
4.
5.
6.
7.
0.773 g/cm3
19,675 g
3,700 mm3
0.756 g/cm3
4.04 g/cm3
0.01651 dm3
6.27 cm3
I know that you want
me to solve them all
with you so that you
can correct your
mistakes, BUT you
need to give them ONE
more shot first.
Corrections due on Monday.
A sample has a mass of 1.02g and
3
a volume of 1.35cm , what is the
density of the nickel?
Density Practice Problems #4
A.) 0.756 g/cm3
B.) 1.38 g/cm3
C.) 1.32 g/cm3
D.) 7.56 g/cm3
A sample has a mass of 1.02g
3
and a volume of 1.35cm , what is
the density of the nickel?
Density Practice Problems #4
What is the density of a material if
its mass 2.02g and its volume is
0.500cm3?
Density Practice Problem #5
A.) 1.01 g/cm3
B.) 4.04 g/cm3
C.) 0.248 g/cm3
D.) 4.48 g/cm3
What is the density of a material if
its mass 2.02g and its volume is
0.500cm3?
Density Practice Problem #5
Pure gold has a density of 19.32
g/cm3. How large (in dm3) would a
piece of gold be if it had a mass of
318.97 g?
Density Practice Problems #6
A.) 16.51 dm3
B.) 1.651 dm3
C.) 0.1651 dm3
D.) 0.01651 dm3
Pure gold has a density of 19.32
g/cm3. How large (in dm3) would a
piece of gold be if it had a mass of
318.97 g?
Density P P #6
How many cm3 would a 55.932 g
sample of copper occupy if it has a
density of 8.92 g/cm3?
Density Practice Problems #7
A.) 0.159 cm3
B.) 499 cm3
C.) 6.27 cm3
D.) 48.9 cm3
3
cm
How many
would a 55.932 g
sample of copper occupy if it has a
density of 8.92 g/cm3?
Density PP #7
Quick Check of Skills
Solve the following on a ½ sheet of paper to turn in to
Mrs. Tarvin in 15 minutes.
1. A) What is the volume (in cm3) of a block of
gold whose density is 19.32 g/cm3 and mass is
48.6 grams?
B) What is the volume in mm3?
2. What is the sum of 3.456m + 0.42m + 3.1m?
3. Divide: 79.23g / 6mL =
4. What is the most difficult thing that we’ve done
so far?
1. A) What is the volume (in cm3) of a
block of gold whose density is 19.32
g/cm3 and mass is 48.6 grams?
1. SET UP THE EQUATION.
2. CROSS MULTIPLY TO FIND THE DENOMINATOR.
3. USE THREE SIG FIGS IN YOUR ANSWER.
1. A) What is the volume (in cm3) of a
block of gold whose density is 19.32
g/cm3 and mass is 48.6 grams?
B) What is the volume in mm3?
1. USE THE ANSWER FROM A IN CM3.
2. MOVE THE DECIMAL ONE PLACE TO THE RIGHT TO
GO FROM CENTI TO MILLI FOR EACH POWER.
3. THEREFORE, MOVE A TOTAL OF THREE SPACES TO
THE RIGHT.
2. What is the sum of 3.456m + 0.42m + 3.1m?
1. LINE UP THE DECIMALS.
2. FIND THE SHORTEST NUMBER. (3.1)
3. DRAW A LINE AT THE END OF 3.1, WHICH MEANS
THAT OUR ANSWER CANNOT GO BEYOND THE
TENTHS PLACE.
4. ADD AND ROUND AT THE LINE TO THE TENTHS
PLACE.
3. Divide: 79.23g / 6mL =
1. COUNT THE NUMBER OF SIG FIGS IN EACH
NUMBER.
2. 79.23 HAS FOUR SIG FIGS.
3. 6 HAS ONLY ONE SIG FIG.
4. THEREFORE, THE ANSWER CAN HAVE ONLY ONE
SIG FIG.
5. DIVIDE AND ROUND TO ONE SIG FIG. USE PLACE
HOLDERS WHERE NEEDED IN FRONT OF THE
DECIMAL.
Tiered Measurement Lab
• You’ll need paper, pencil, and a calculator.
• You must apply metric conversions,
measurement skills (using an estimated digit),
density, and sig fig calculations.
• Six stations are available, and each is worth a
certain number of points.
• You need to earn 60 points. No extra credit is
available.
• Record EACH measurement, and show ALL
calculations.
• Lab is due tomorrow.
Use the data table to give you instructions. Be sure
to label your work with station numbers. Record
ALL measurements in each unit required. Show
ALL calculations with each unit required.
Convert the density of 0.58 g/mL to lb/gallon.
(1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb)
Convert the density of 0.58 g/mL to lb/gallon.
(1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb)
Convert the density of 0.58 g/mL to lb/gallon.
(1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb)
Convert the density of 0.58 g/mL to lb/gallon.
(1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb)
Convert the density of 0.58 g/mL to lb/gallon.
(1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb)
If a pound of apples costs $0.79,
then 5.3 lbs will cost _________.
Give your answer to TWO
decimal places which is
customary with money.
1849 yards = __________ miles
Hint: 5280 ft = 1 mile
Give your answer to 4 sig figs.
If Boston and New York City are
190 miles apart, then the
distance between the two cities
is _______ km.
Hint: 1 km = 0.621 miles
Give your answer to TWO sig
figs.
If a pound of apples costs $0.79,
then a shopper with $2.00 will be
able to purchase ________ lbs
of apples.
Give your answer to THREE sig
figs.
If a US car advertisement brags
that an SVU gets 26 miles/gallon
on the highway, then the same car
would be described in Europe as
getting ___________ km/L.
Hint: 1 L = 1.057 qt; 4 qt = 1 gal;
1 km = 0.621 miles
Give you answer to TWO sig figs.