•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
– Conversions
Oops!
• Temperature
– Kelvin & Celsius
Moving the Decimal
T // G // M // k h D base d c m // µ // n // p // f
Practice.
1. 33 km = _____________ mm
2. 175 nm = ____________ Dm
3. 0.5 GL = _____________ cL
Evaluate. (True or false?)
1. 453 µg = 0.00453 hg
2. 16 Mbytes = 0.016 Gbytes
33 km = ________ mm
A.) 0.000033 mm
B.) 0.033 mm
C.) 33,000 mm
D.) 33,000,000 mm
175 nm = _______ Dm
A.) 0.000 000 175
B.) 0.0 000 000 175
C.) 1,750,000,000
D.) 1,750,000,000,000
0.5 GL = ______ cL
A.) 5,000,000 cL
B.) 50,000,000 cL
C.) 50,000,000,000 cL
D.) 0.000 000 000 005 cL
453 micrograms = 0.00453 hectograms
A.) True
B.) False
16Mbytes = 0.016Gbytes
A.) True
B.) False
• Complete the 1-4 Practice
Problems (1-10) tonight.
• Metric System Quiz - Friday
Sample Element Quiz Questions
1.
2.
3.
4.
5.
6.
Co _______________________
Cr ________________________
Sn _______________________
Copper ____________________
Sodium ____________________
Iron ________________________
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)
b)
c)
Since cm3 = mL, 32,000cm3 = 32,000 mL.
Move the decimal 3 spaces to the left to go from milli to liters.
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.
2.
3.
4.
Density = mass / volume
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.
Convert 2.5 dm3 to cm3. Move the decimal to the right THREE spaces.
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 a
volume of 1.35cm3, 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 and a
volume of 1.35cm3, 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
3
cm
How many
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
How many cm3 would a 55.932 g
sample of copper occupy if it has a
3
density of 8.92 g/cm ?
Density PP #7
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
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 in the fall 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.
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
79.2 meters
4. 18 meters
2. 7.33 meters
3. 17.3 meters
5. 675 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
A
123456
6 sig figs!
•
•
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
54321
56,043,000
A
5 sig figs!
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
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.
2.
3.
SET UP THE EQUATION.
CROSS MULTIPLY TO FIND THE DENOMINATOR.
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.
2.
3.
USE THE ANSWER FROM A IN CM3.
MOVE THE DECIMAL ONE PLACE TO THE RIGHT TO GO FROM CENTI TO MILLI FOR
EACH POWER.
THEREFORE, MOVE A TOTAL OF THREE SPACES TO THE RIGHT.
2. What is the sum of 3.456m + 0.42m + 3.1m?
1.
2.
3.
4.
LINE UP THE DECIMALS.
FIND THE SHORTEST NUMBER. (3.1)
DRAW A LINE AT THE END OF 3.1, WHICH MEANS THAT OUR ANSWER CANNOT GO
BEYOND THE TENTHS PLACE.
ADD AND ROUND AT THE LINE TO THE TENTHS PLACE.
3. Divide: 79.23g / 6mL =
1.
2.
3.
4.
5.
COUNT THE NUMBER OF SIG FIGS IN EACH NUMBER.
79.23 HAS FOUR SIG FIGS.
6 HAS ONLY ONE SIG FIG.
THEREFORE, THE ANSWER CAN HAVE ONLY ONE SIG FIG.
DIVIDE AND ROUND TO ONE SIG FIG. USE PLACE HOLDERS WHERE NEEDED IN FRONT
OF THE DECIMAL.
•Organized method of problemsolving
•Used in chemistry, physics,
engineering, and medicine
•Communicates the path to
scientists that follow your work
•Records your own path for your
future use
•Calculate the number of minutes in 3.61 hours.
*Note: Use the number given in the question to determine the number of sig figs in your
answer.
•Calculate the number of minutes in 3.61 hours.
*Note: Use the number given in the question to determine the number of sig figs in your
answer.
•Calculate the number of minutes in 3.61 hours.
*Note: Use the number given in the question to determine the number of sig figs in your
answer.
How many centimeters are in 4.2 inches?
*Note: Use the number given in the question to determine the number of sig figs in your
answer.
How many centimeters are in 4.2 inches?
*Note: Use the number given in the question to determine the number of sig figs in your
answer.
Calculate the number of seconds in two weeks.
Calculate the number of seconds in two weeks.
Calculate the number of seconds in two weeks.
Calculate the number of seconds in two weeks.
Calculate the number of seconds in two weeks.
Convert the density of 0.58 g/mL to lb/gallon.
L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb)
(1
Convert the density of 0.58 g/mL to lb/gallon.
L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb)
(1
Convert the density of 0.58 g/mL to lb/gallon.
L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb)
(1
Convert the density of 0.58 g/mL to lb/gallon.
L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb)
(1
Convert the density of 0.58 g/mL to lb/gallon.
L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb)
(1
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.