Name:
Period:
Date:
PAP Scientific Measurement UNIT Booklet
How do we measure how much
matter is present in a sample?
Student Goal:
Read, analyze and interpret graphs and other representations of data
Table of Contents
Topic
Page Number
Measuring with Precision and Accuracy
Precision vs. Accuracy
Expressing errors in measurements
Rules for calculating significant numbers
Calculating with Sig Figs
Rounding numbers rules
Reading Instruments
2-3
3-4
7
4-5
5
9
6-7
Dimensional analysis
Dimensional analysis steps
Sample and practice problems
8 - 10
8
9- 10
Scientific Notation
11
Math Skills Review
Manipulating variables review
Chemistry Math Review Practice Problems
12-13
12
13
Density
14 - 18
14
14
15
16
16 - 17
17 - 18
What is Density?
How is density related to an object’s ability to float?
How do I solve problems related to density?
Density example problems
Deriving Information from a Graph Using Density
DENSITY PRACTICE PROBLEMS
Study Guide for Measurement Unit
18 - 21
Answers cannot be more precise that the
least precise of the measurements.
1
Name:
Period:
http://www.chemistryland.com/CHM130S/02-MMM/Measure/Measuring.htm
Date:
OBJECTIVE: you will be able to understand and be able to apply the concepts of accuracy and precision.
PRECISION VERSUS ACCURACY
Define precision.
Define accuracy.
1. Woody and Buzz ran an experiment to the spring constant of Slinky Dog dropping his back of a
building and measuring the height he sprung back up. Their trials showed that
Slink had the following measurements of force: 0.333 N, 0.454 N, and 0.222 N in their three trials.
Hamm and Rex ran their own trials, and got 0.788 N, 0.780 N, and 0.788 N.
Slinky told them his actual force was actually 0.350 N.
a. What team was more precise? Why?
b. What team was more accurate? Why?
2. Use box #2 to draw a picture that is more precise but less accurate than shown in picture #1.
3.
Use the empty box to draw a picture that is more precise and accurate than in picture #1.
Figure 1
2
Figure 2
Figure 3
4. Determine the accuracy and precision (Poor/Good) represented by each group
of darts in the figures above. Explain your choices using complete sentences.
Name:
Period:
Figure 1
Date:
Figure 2
Figure 3
Precision?
Accuracy?
4. Three students made multiple weighings of a copper cylinder, each using a different balance. Describe
the accuracy and precision of each student’s measurements if the correct mass of the cylinder is 27.32
g. Hint: find the average mass for each student.
Weighing 1
Weighing 2
Weighing 3
Weighing 4
Brian
27.92
26.99
27.40
27.50
Mass of Cylinder
Calvin
27.98
27.96
27.97
27.99
Evelyn
27.30
27.33
27.32
27.31
Brian:
Calvin:
Evelyn:
Expressing Errors in Measurement:
Scientists often express their uncertainty and error in measurement by giving a percent error. The
percent error is defined as:
PRACTICE PROBLEMS
1. While doing a lab, a student found the density of a piece of pure aluminum to be 2.85g/cm 3. The
accepted value for the density of aluminum is 2.70 g/cm 3. What was the student's percent error?
2. A student measured the specific heat of water to be 4.29 J/g · Co. The literature value of the
specific heat of water is 4.18 J/g · Co. What was the student’ percent error?
3
Name:
Period:
Date:
OBJECTIVE: you will be able to measure with accuracy and precision.
Significant Figures:
http://www.chemistryland.com/CHM130S/02-MMM/SigFigs/SignificantNumbers.html
A.
B.
C.
D.
RULES FOR CALCULATING SIGNIFICANT FIGURES
All Non –zero Digits ARE Significant (ie 1,2,3,4,5,6,7,8,9)
All Leading Zeros ARE NEVER Significant (ie 0.000279)
All Middle Zeros ARE Significant (ie 204)
All Trailing Zeros ARE significant IF AND ONLY IF there is a DECIMAL in the Number (ie 2.0)
EXAMPLE PROBLEMS
1. 23.50
2. 402
_____________sig figs.
Rule (s) __________
_____________sig figs.
Rule (s) __________
3. 5,280
_____________sig figs.
Rule (s) __________
4. 0.080
____________sig figs.
Rule (s) __________
PRACTICE PROBLEMS I
How many significant figures are there in each of the following numbers?
1)
2)
3)
4)
5)
6)
7)
27
________________
2700
________________
2700.
________________
2700.0 ________________
3
2.7 x 10 ________________
3
2.70 x 10 ________________
3
2.700 x 10
________________
8) .524
________________
9) 0.0524 ________________
10) 0.0524 ________________
11) 0.05240 ________________
-1
12) 5.24 x 10
________________
-2
13) 5.24 x 10
________________
-2
14) 5.240 x 10
________________
Another way to find out the number of significant numbers:
The Pacific-Atlantic Rule:
_ _ _ _ _ _ Ocean
_ _ _ _ _ _ _ Ocean
______________
______________
To find the number of significant figures:
1. If the decimal point is
_________, start on the ____________ side.
If the decimal point is
_________, start on the ____________ side.
2. Start counting digits with the first ______________ number that you reach. Then count all the
digits in the direction determined above.
4
Name:
Period:
Date:
PRACTICE PROBLEMS II
How many significant figures are in the numbers listed below?
_____ 3.9802 L
_____ 10000 Kg
_____ 40200 mL
_____ 2005 N
_____ 0.005709 g/mL
_____ 298.009 atoms
_____ 4.0001 cm
_____ 284 moles
Calculating with Sig Figs
_
Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the
answer.
 (This is the measurement that is the LEAST precise)
–
Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.
• (This is the measurement that is the LEAST precise)
Addition/Subtraction and Multiplication/Division Rules
Add/Subtract:
COUNT LEAST AMOUNT OF DECIMAL PLACES
Multiply/Divide: COUNT LEAST AMOUNT OF SIG FIGS
Rounding rules
 Look at the number behind the one you’re rounding.
 If it is 0 to 4 don’t change the number you want to round.
 If it is 5 to 9 make change the number you want to round
to number bigger.
PRACTICE PROBLEMS III
Perform the following calculations using the correct number of significant figures:
1. 2.98+4.1
5. 3.098 + 238
2. 3.094-0.987465
6. 459.0 / 45
3. 452÷50
7. 2901 × 25.3
4. 2.7 × 6.0
8. 2.01 + 3
5
Name:
Period:
Date:
READING INSTRUMENTS
1. Directions: Read the following instruments. Don't forget to include the correct number of
significant figures and units.
a. _________ b. _________
c. _________
d. _________
2. You have two pieces of equipment. One reads 47 ml, and the other reads 47.00 ml.
Explain why these measurements are different in terms of the marks found on each instrument
3. Name the following laboratory apparatus, and circle the one that will give the most precise results for
measuring the volume of a liquid.
c)
a)
b
d)
6
3)
Name:
Period:
Date:
https://www.youtube.com/watch?v=uZ0ILIG_l7w
7
Name:
Period:
Date:
OBJECTIVE: To be able to change units of measurement by using dimensional analysis.
DIMENSIONAL ANALYSIS.
http://www.chemistryland.com/CHM130S/02-MMM/DimensionalAnalysis/DimensionalAnalysis.htm
Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a
problem-solving method that uses the fact that any number or expression can be
multiplied by one without changing its value. It is a useful technique. The only danger is
that you may end up thinking that chemistry is simply a math problem - which it definitely
is not.
Unit factors may be made from any two terms that describe the same or equivalent
"amounts" of what we are interested in. For example, we know that
1 inch = 2.54 centimeters
We can make two unit factors from this information:
Now, we can solve some problems. Set up each problem by writing down what you need
to find with a question mark. Then set it equal to the information that you are given. The
problem is solved by multiplying the given data and its units by the appropriate unit factors
so that only the desired units are present at the end.
(1) How many centimeters are in 6.00 inches?
(2) Express 24.0 cm in inches.
Dimensional Analysis Steps:
1. Begin by setting up the given value as a fraction.
2. Add a second term, being sure that the unit in the numerator of the first term
ends up in the denominator of the second term, so that it can divide out (or vice
versa, if the starting unit is in the denominator).
3. Be sure that the quantities in the numerator and denominator of each term are
equivalent, even though their units are different.
4. Be sure to stop adding terms when you reach the unit of interest!
5. Cancel out any units that can be.
6. Solve.
8
Name:
Period:
Date:
Dimensional analysis problems always involve a Given value and one or more conversion factors that
allow you to determine the Desired value.
Conversion factor
Known Value (Given units)
(Desired units)
(Given units)
Scientists generally work in metric units. Common prefixes used are the following:
Prefix
megakilocentimillimicronano-
Abbreviation
M
k
c
m
n
Meaning
106
103
10-2
10-3
10-6
10-9
Example
1 megameter (Mm) = 1 x 106 m
1 kilogram (kg) = 1 x 103 g
1 centimeter (cm) = 1 x 10-2 m
1 milligram (mg) = 1 x 10-3 g
1 micrometer ( g) = 1 x 10-6 g
1 nanogram (ng) = 1 x 10-9 g
Basic Units in the metric system: liter, grams, meter
Useful conversion factors:
LENGTH
1 inch = 2.54 cm
1 ft = 12 inches
1 mile = 5280 feet
1 mile = 1.61 km
1 m = 1.09 yards
MASS
1 lb = 454 g
1 kg = 2.21 lb
1 lb = 16 oz
FLUID VOLUME
1 L = 1.06 qt
4 qts = 1 gal
1 qt = 2 pints
1 pint = 2 cups
Example problems:
How many quarters in $120 dollars?
Unkown = quarters;
Knows:
?
=
=
How many seconds are in 2.0years?
Unknown: seconds;
?
=
9
Knowns:
1 year
1 day
1 hour
1 minute
_
=
=
=
=
365 days
24 hours
60 minutes
60 seconds
=
Name:
Period:
Date:
How many kilograms in 240.0 pounds?
Unkown =
?
Knows:
=
=
PRACTICE PROBLEMS
Use the following information for questions 1 through 4:
Knowns:
3 blarps = 7 glorps
8 glorps = 17 trangs
1. How many slurps are in 107 kilps?
2. How many blarps are in 73 trangs?
3. How many kilps are in 3 blarps?
4. How many glorps are in 245 trangs?
10
11 trangs = 5 slurps
2 slurps = 23 kilps
Name:
Period:
Date:
OBJECTIVE: To be able to use scientific notation.
SCIENTIFIC NOTATION http://www.purplemath.com/modules/exponent3.htm
Scientific notation is __________________________________________________________
__________________________________________________________________________
How to express a number in scientific notation:
1. Move the decimal until there is one number to the _____________ of the decimal. You
should now have a number that is between 1 and 10.
2. Count the number of places you have moved the decimal from its original location. This
will be the ______________________.
3. If you moved the decimal to the __________, the exponent will be _______________.
4. If you moved the decimal to the _________, the exponent will be _______________.
Examples: Express the following number in scientific notation:
1)
2)
3)
4)
5)
61,500
0.0000568
321
64,960,000
0.07085
_________________
_________________
_________________
_________________
_________________
How to change a number back from scientific notation:
1. Look at the exponent. If it is ____________, move the decimal point to the _________.
2. If it is ________________, move the decimal point to the ______________.
3. Move the decimal the number of spaces specified by the ______________________.
Examples: Convert the following numbers from scientific notation to regular numbers:
1)
2)
3)
4)
5)
1.09 x 103
4.22715 x 108
3.078 x 10-4
9.004 x 10-2
5.1874 x 102
_________________
_________________
_________________
_________________
_________________
Convert the following numbers between standard notation and scientific notation.
11
Name:
Period:
OBJECTIVE: you will be able to manipulate equations to isolate variables.
12
Date:
Name:
Period:
Date:
Chemistry Math Review Practice Problems
Answer the following questions
1)
2+4x3=
2)
4+2x3=
3)
2x4+3=
4)
2x4+3=
5)
40 + 20 =
10
6)
20 + 40 =
10
7)
40 + 20 =
10
8)
20 + 40 =
10
9)
(4 + 3) ÷ 6 =
10)
Solve the following equations for x
11) 2x = 8
4+3÷6=
12) 2 = 8x
13)
x
8
2
14)
x
2
8
15)
2
8
x
16)
8
2
x
18)
x y
4
z
17)
x
y
4
z
Answer the following questions
19) (3.0 x 104) + (6.3 x 105)
13
20. (3.0 x 108) x (6.3 x 107)
Name:
Period:
Date:
OBJECTIVES: you will be able to organize, analyze, evaluate, make inferences, and predict trends
from data.
Density
OBJECTIVE: you will be able to understand and apply the concept of density.
What is Density?
DEFINITION
FORMULA
Density 
Mass
Volume
or D 
m
V
DENSITY
What You are Measuring?
Mass (m)
Volume (V)
Density (D)
GRAPH
Possible Units
UNITS
How is density related to an object’s ability to float?
In the beaker below, draw your observations from today’s demonstration.

If an object is less dense, which means that its density is a
object will float.
14
number, then the
Name:
Period:
Date:
Example problem
The table shows some properties of four different substances. The picture shows a solid sphere of one of
the four substances in a water-ethanol solution, which has a density of
0.9199g/mL. The sphere is more likely composed of which substance?
A.
Substance Q
B.
Substance R
C.
Substance S
D.
Substance T
Your Answer and Explanation:
How do I solve problems related to density?
Use the G.U.E.SS method
G
U
E
S
S
Given
Unknown
Equation
Substitute
Solve
& box
EXAMPLE PROBLEMS
1. What is the density of a piece of metal if the mass of the metal is 562 grams, and it occupies 44.9mL?
2. A box is determined to have a mass of 15.50g. Its dimensions are determined to be 2.4cm x 5.6cm x 6.70cm.
What is the density of this box? Would this box float in water (D = 1.00g/mL)?
What is water displacement and how do I use it to find the density of an object?
Water displacement is used to determine the
of an object by looking at the
change in water level in a graduated cylinder.


How do I know when to use it?
Water displacement is usually used for irregular objects.
In a problem, look for key words such as:
15
Name:
Period:
Date:
o
o
Example Problems
1. Omar believes that he found a small piece of gold in the bus parking lot. After getting permission from Ms.
Head to perform the experiment, Omar puts on his safety goggles and finds the mass of his object to be
45.2g. He then places the object in a graduated cylinder and notes that the water level rises 5.6mL. If the
density of gold is 19.3g/cm3, did Omar find gold? Use calculations to justify your answer.
2. A student was unable to locate a ruler to measure a second metallic object. Its mass was 28.90g. He
obtained a graduated cylinder which initially contained 35.0mL of water. When the metallic cylinder was
placed into the graduated cylinder, the water level rose to 45.7mL. What is the identity of this metallic
object? Use calculations to justify your answer.
Silver
Lead
Gold
Aluminum
Density (g/cm3)
10.5
11.34
19.3
2.70
Deriving Information from a Graph Using Density
Density relates a substance’s mass to its volume. If you have several samples of a single substance of
different sizes, and measure the volume and mass of each sample, a plot of each measurement on a graph will
produce a straight line.
1. Will the line’s slope be positive or negative? To answer, think about how the mass changes as the size
(volume) of the sample increases.
2. The graph at right is the plot of the volumes and
masses of the three pure gold bars. What is the
density of gold?
3. Use the graph to determine the mass of 4 cm3 of
gold.
4. Use your answer to #1 to determine:
A. The mass of 8 cm3 of gold
B. The volume of 200 grams of gold
16
Name:
Period:
Date:
5. Draw a line through the 3 points of the graph. The line should originate at (0,0). Does that make sense
since density relates mass and volume? What mass would you expect a substance to have at zero
volume? Would you expect all density plots to originate at (0,0)? Why/ why not?
6. What does the graph tell you about density and sample size? Does the density of a substance change
with sample size, or will it always be the same for any one substance? Explain.
7. What is the relationship between density and slope on a
mass vs volume graph?
The illustration at right shows lines plotted from the data of three
metal samples.
8. Which metal, A, B, or C has the highest density? Explain
your reasoning.
DENSITY PRACTICE PROBLEMS
You must show all work using the GUESS method to receive full credit. “I did it in the calculator”
does not count as work!  Report your answer with the correct units and the proper number of
significant figures.
1.
What is the density of gas that occupies 4.5L and has a mass of 2.1g?
2.
How much space would a 2.75g sample of a substance occupy, if it has a density of 0.993g/cm3?
3.
What is the mass of an object that has a density of 5.0g/cm3 and a volume of 8.4cm3?
4.
What is the mass of 20.6cm3 of iron?
17
Name:
Period:
Date:
5. What is the density of a 32.1g metallic box if its dimensions are 2.5cm by 6.0cm by 3.1cm?
6.
A cube has a side that measures 8.0cm. The cube also has a mass of 400.0g. Would this cube float?
Explain your answer.
7.
Initially a student had a graduated cylinder with 21.4mL of water. After a 4.67g object is submerged in the
water, the level reads 30.5mL. What is the density of the object?
8.
A student has a piece of metal that has a mass of 45.3g and has a volume of 2.35cm3. What is the identity
of the metal?
Metal
Density (g/cm3)
Silver
10.5
Lead
11.34
Gold
19.3
Iron
7.87
9.
According to the graph below, what is the density of the object? How did you find it?
Study Guide for Unit 1 Test: Safety and Measurement
Safety
6. What should you do if you spill an acid (i.e. what is different about spilling an acid versus other chemicals)?
7. Where do we meet if we have a fire drill?
8. What should you do before starting ANY lab?
9. What should you do before leaving ANY lab?
18
Name:
Period:
19
Date:
Name:
Period:
Date:
Measurement
10. Express the following numbers in scientific notation.
a. 10, 200
c. 0.102
b. 205,000,000
d. 0.000000000103
11. Express the following numbers in ordinary notation.
a. 1.2x101
c. 6.801x105
b. 3.45x10-8
d. 7.4405x10-3
12. How many significant figures are present in each of the following measurements?
13.
a. 0.0102m
d. 50500s
b. 2.00m
e. 20L
c. c. 20.L
f. 2.30x103km
Perform the following calculations and report the answers with the correct number of significant figures.
a. 12.1m + 0.123m + 0.12m
b. 7.50cm x 1.234cm
c. 10200s – 3000s
d.
20
1500000 g
30300mL
Name:
Period:
Date:
Dimensional analysis
14. How many kilograms are equal to350 grams?
15. How many pounds are equal to350 grams?
16. How many miles are in 44,982 inches?
17. A student determines the density of copper to be 9.19g/cm3. Calculate the percent error for this student’s
experimental data if the accepted value for the density of copper is 8.94g/cm3 .
18. For each of the following students, explain whether their data is accurate, precise, both, or neither. Assume
the accepted value for their measurement is 458.5.
Student Name
Zoe
Jo
Melissa
Trial #1
458.43
462.78
468.47
Trial #2
458.5
451.33
468.52
Trial #3
458.49
475.89
468.45
Zoe:
_________________________________________________________________
Joe:
_________________________________________________________________
Melissa: ________________________________________________________________
Density
1. How much space would a 12.75g sample of a substance occupy if it has a density of
4.993g/cm3?
2. What is the mass of 20.6cm3 of lead if lead has the density of 11.34g/cm3 ?
3. What is the density of a 52.1g metallic box if its dimensions are 5.533cm by 6.00cm by
3.12cm?
4. Initially a student had a graduated cylinder with 11.4mL of water. After a 8.67g object is
submerged in the water, the level reads 30.5mL. What is the density of the object?
21