Name: Period: Date:
Prep-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 2 - 3
Precision vs. Accuracy 3 - 4
Expressing errors in measurements 7
Rules for calculating significant numbers 4 - 5
Calculating with Sig Figs 5
Rounding numbers rules 9
Reading Instruments 6 - 7
Dimensional analysis 8 - 10
Dimensional analysis steps 8
Sample and practice problems 9- 10
Scientific Notation 11
Math Skills Review 12-13
Manipulating variables review 12
Chemistry Math Review Practice Problems 13
Density 14 - 18
What is Density? 14
How is density related to an object’s ability to float? 14
How do I solve problems related to density? 15
Density example problems 16
Deriving Information from a Graph Using Density 16 - 17
Density Practice Problems 17 - 18
Study Guide for Measurement Unit 18 - 21
2Name: Period: Date:
Answers cannot be more precise that the
least precise of the measurements.
http://www.chemistryland.com/CHM130S/02-MMM/Measure/Measuring.htm
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 / Figure 2 / Figure 3Precision?
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.
Mass of CylinderBrian / Calvin / Evelyn
Weighing 1 / 27.92 / 27.98 / 27.30
Weighing 2 / 26.99 / 27.96 / 27.33
Weighing 3 / 27.40 / 27.97 / 27.32
Weighing 4 / 27.50 / 27.99 / 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/cm3. The accepted value for the density of aluminum is 2.70 g/cm3. 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?
OBJECTIVE: you will be able to measure with accuracy and precision.
Significant Figures:
http://www.chemistryland.com/CHM130S/02-MMM/SigFigs/SignificantNumbers.html
Rules for Calculating Significant Figures
A. All Non –zero Digits ARE Significant (ie 1,2,3,4,5,6,7,8,9)
B. All Leading Zeros ARE NEVER Significant (ie 0.000279)
C. All Middle Zeros ARE Significant (ie 204)
D. All Trailing Zeros ARE significant IF AND ONLY IF there is a DECIMAL in the Number (ie 2.0)
Example problems
1. 23.50 ______sig figs. Rule (s) ______
2. 402 ______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?
2Name: Period: Date:
1) 27 ______
2) 2700 ______
3) 2700. ______
4) 2700.0 ______
5) 2.7 x 103 ______
6) 2.70 x 103 ______
7) 2.700 x 103 ______
8) .524 ______
9) 0.0524 ______
10) 0.0524 ______
11) 0.05240 ______
12) 5.24 x 10-1 ______
13) 5.24 x 10-2 ______
14) 5.240 x 10-2 ______
2Name: Period: Date:
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.
Practice Problems II
How many significant figures are in the numbers listed below?
_____ 3.9802 L_____ 40200 mL
_____ 0.005709 g/mL
_____ 4.0001 cm / _____ 10000 Kg
_____ 2005 N
_____ 298.009 atoms
_____ 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 RulesAdd/Subtract: COUNT LEAST AMOUNT OF DECIMAL PLACES
Multiply/Divide: COUNT LEAST AMOUNT OF SIG FIGS
Practice Problems III
Perform the following calculations using the correct number of significant figures:
1. 2.98+4.12. 3.094-0.987465
3. 452÷50
4. 2.7 × 6.0 / 5. 3.098 + 238
6. 459.0 / 45
7. 2901 × 25.3
8. 2.01 + 3
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.
2Name: Period: Date:
a) 3)
b d)
https://www.youtube.com/watch?v=uZ0ILIG_l7w
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.
Scientists generally work in metric units. Common prefixes used are the following:
Prefix / Abbreviation / Meaning / Examplemega- / M / 106 / 1 megameter (Mm) = 1 x 106m
kilo- / k / 103 / 1 kilogram (kg) = 1 x 103g
centi- / c / 10-2 / 1 centimeter (cm) = 1 x 10-2m
milli- / m / 10-3 / 1 milligram (mg) = 1 x 10-3g
micro- / / 10-6 / 1 micrometer (g) = 1 x 10-6g
nano- / n / 10-9 / 1 nanogram (ng) = 1 x 10-9g
Basic Units in the metric system: liter, grams, meter
Useful conversion factors:
LENGTH / MASS / FLUID VOLUME1 inch = 2.54 cm / 1 lb = 454 g / 1 L = 1.06 qt
1 ft = 12 inches / 1 kg = 2.21 lb / 4 qts = 1 gal
1 mile = 5280 feet / 1 lb = 16 oz / 1 qt = 2 pints
1 mile = 1.61 km / 1 pint = 2 cups
1 m = 1.09 yards
Example problems:
How many quarters in $120 dollars?
Unkown = quarters; Knows:
? = =
ow many kilograms in 240.0 pounds?
Unkown = Knows:
? = =
Practice problems
Convert the following using the Dimensional Analysis solving problems method. SHOW ALL WORK.
1. ______meters = 177 millimeters
2. ______grams = 9.3 kilograms
3. ______mL = 2.2 L
4. ______mL = 500 cm3
5. ______dm3 = 4.0 L
6. ______cm = 3.34 m
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) 61,500 ______
2) 0.0000568 ______
3) 321 ______
4) 64,960,000 ______
5) 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) 1.09 x 103 ______
2) 4.22715 x 108 ______
3) 3.078 x 10-4 ______
4) 9.004 x 10-2 ______
5) 5.1874 x 102 ______
Convert the following numbers between standard notation and scientific notation.
OBJECTIVE: you will be able to manipulate equations to isolate variables.
Chemistry Math Review Practice Problems
Answer the following questions
1) 2 + 4 x 3 = 2) 4 + 2 x 3 =
3) 2 x 4 + 3 = 4) 2 x 4 + 3 =
5) 40 + 20 = 6) 20 + 40 =
10 10
7) 40 + 20 = 8) 20 + 40 =
10 10
Solve the following equations for x
9) 2x = 8 10) 2 = 8x
11) 12)
13) 14)
15) 16)
OBJECTIVE:
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 / Formulaor
Graph / What You are Measuring? / Possible Units
Mass (m)
Volume (V)
Density (D)
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 number, then the object will float.
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 / SGiven / 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?