Accuracy vs. Precision:

____________________- o How close a measurement is to the true or known value

____________________- o Several measurements very close to one another
Percent Error: o Experimental (actual) = the value determined from lab data o Theoretical (accepted) = the standard, true, or accepted value
Exact vs. Inexact Numbers:

____________________- o Conversion factors & counting o Ex) There are exactly 5280 ft in 1 mile…12 eggs in 1 dozen…2.54 cm in 1 inch

____________________- o Measurements from equipment with limitations

o Ex) mass using a balance…volume using a graduated cylinder…etc.
Uncertainty in Measurements:

Different pieces of equipment have different uses and different degrees of accuracy o All measurements must be reported with the last digit being uncertain (1 degree of uncertainty) o The volume measurement in the picture to the right should be reported with 1 degree of uncertainty, as
__________________.
Significant Figures (Sig Figs):
 The term significant figures refers to digits that were “measured” or ____________ #s.

We pay attention to sig figs so we do not overstate the accuracy of our calculations
> Sig Fig Rules:
1) All non-zero digits [1-9] are significant
2) Zeroes between any non-zero digits are significant [ ex: 101 ]
3) Zeroes at the beginning of a number, before any non-zero digits, are NEVER significant
[ ex: 0.082 ]
4) Zeroes at the end of a number are significant ONLY if the number contains a decimal point
[ ex: 35.0 vs. 350 vs. 350. ]
> Practice Counting Sig. Figs :
1) ___________ 0.0034567 g
4) ___________ 598.300 K
2) ___________ 2.97 mL
3) ___________ 6.700 x 10 3 m
5) ___________ 78,000 mg
6) ___________ 9020 cm
> Calculations w/Sig. Figs:

Addition or Subtraction – round the answer off to the least number of decimal places
Ex) 20.42 g + 7.9764 g + 102.3 g = _________________________
Reported Answer = ______________________ o Practice +/ – w/Sig. figs:

1) 15.002 cm + 24.1104 cm = ________________________________
2) 22.35 kg – 0.154 kg = __________________________________
3) 100.0 g – 23.73 g = __________________________________
4) 2.030 mL – 1.870 mL = ___________________________________

Multiplication or Division – round the answers off to the least number of sig. figs.
Ex) (6.221 cm)(5.2 cm) = __________________________
Reported Answer = _________________________ o Practice x/

w/Sig. figs:
1) 75.246 g / 6.33 mL = _____________________________
2) (16.00 cm)(2.5 cm)(3.66 cm) = ___________________________
3) (3.24 m)(7.00 m) = ____________________________
4) 710 m / 3.0 s = _____________________________

Mixed Operations – always follow PEMDAS; count sig. figs as you go to get it correct
Ex) (44.739 g – 36.21 g) = ____________________________
1.3 mL
Reported Answer: ___________________________

A. Indicate the number of sig figs, then round each to the number of significant figures indicated.
Example:
1.234 has __4__ significant figures and, rounded to 2 significant figures, is ___1.2_____
1) 0.6034 has _____ significant figures and, rounded to 2 significant figures, is ___________
2) 12,700 has _____ significant figures and, rounded to 2 significant figures, is __________
3) 12,700.00 has _____ significant figures and, rounded to 1 significant figures, is ___________
4) 0.000983 has _____ significant figures and, rounded to 2 significant figures, is ___________
5) 123342.9 has _____ significant figures and, rounded to 5 significant figures, is ___________
6) 6.023 x 10 23 has _____ significant figures and, rounded to 2 significant figures, is ___________
7) 0 .
005600 has _____ significant figures and, rounded to 1 significant figures, is ____________
8) 10000.5006 has _____ significant figures and, rounded to 5 significant figures, is ___________
9) 2.0 x 10 -3 has _____ significant figures and, rounded to 1 significant figures, is ___________
10) 3.456110 has _____ significant figures and, rounded to 3 significant figures, is ___________
B. Given the following calculations, write the given answers with the appropriate number of sig figs.

Example :
6.00 x 3.00 = 18 The answer should be ______18.0_____
1) 23 + 46 = 69
2) 23.0 + 46.0 = 69
3) 253 + 345.8 = 598.8
4) 56 – 35 = 21
5) 56.00
– 35.0 = 21
6) 46 x 12 = 552
7) 3.24 x 5.63 = 18.2412
The answer should be 1) _______________
The answer should be 2) _______________
The answer should be 3) _______________
The answer should be 4) _______________
The answer should be 5) _______________
The answer should be 6) _______________
The answer should be 7) _______________
8) (2.355 + 2.645) x 10.00 = 50
9) 654

32 = 20.4375
The answer should be 8) _______________
The answer should be 9) _______________
10) 0.024 x .063 = 1.512 x 10 -03 The answer should be 10) _______________
C. Assume all the numbers in these problems are “measured” numbers. Perform all the calculations. Make sure that your answers have the correct number of significant figures.
1. 3.9 x 1.25 =
2. 12.625 ÷ 2.03 =
3. 3.1895 – 1.32 =
4. 300.6 =
(12.2 + 1.125)
5. 150 x 2.13 =
6. 149 + 8.01

7. 44,000 ÷ 11 =
8. (18.79 x 12.1) =
13.125
9. (18.8 – 12.1) =
3.1
10. (4.23 x 10 3 )(4.23 x 10 -3 ) =
11. 150. X 2.13 =
A. Use the rules for significant figures when adding and subtracting:
Answer before rounding Final Answer
Example: 134.8 + 27.67 = 162.47 162.5
1. 109.5 + 24.02 = ____________________ _____________________
2. 66.341 + 902.10 = ____________________ _____________________
3. 88.001 – 56.7 = ____________________ _____________________
4. 5696.10 – 34.0010 = ____________________ _____________________
5. (32.1 + 354.98) – 224.775 = ____________________ _____________________
6. 412.667 + 22.11 + 15.6 = ____________________ _____________________
7. 5286.445
– 26.0005 – 13.112 = ____________________ _____________________
8. 3.468 – (2.4 + 13.67) – 117.11119 = ____________________ _____________________
B. Use the rules for significant figures when multiplying and dividing:

Answer before rounding Final Answer
Example: 34.8 x 27.67 = 962.916 963
9. 109.5 x 24.02 = ____________________ _____________________
10. 66.341 x 902.10 = ____________________ _____________________
11. 88.001

56.7 = ____________________ _____________________
12. 5696.10 x 34.0010 = ____________________ _____________________
13. (32.1 x 354.98)

224.775 = ____________________ _____________________
14. (1.68 x 2.45)

5.912 = ____________________ _____________________
15. 432.721

13.2467

21.44 = ____________________ _____________________
Qualitative vs. Quantitative:

____________________- o Observations which reflect a physical description of data o Ex) color, odor, texture, state of matter

____________________- o Measurements that include numerical quantities & data o Ex) mass, volume, density, length, time
SI Base Units:
*
*
*
*
*
Physical Quantity
Mass
Length
Time
Temperature
Amount of Substance
Electric Current
Luminous Intensity
Name of Unit ampere candela

Derived Units o Two or more SI base units combined o Example: Density = mass = kg .
Volume m 3
Scientific Notation:
Abbreviation
A cd


Format: M x 10 n o M is a # between 1-9 o n is an integer

#s SMALLER than 1 = negative exponent (ex: 0.00000765 = ______________)

#s BIGGER than 1 = positive exponent (ex: 2,340,000,000 = ______________)
Temperature:

Two definitions- o A measure of the average _________________ energy of particles in a sample o A measure of how much ___________ is in an object

Temperature Conversions- o K = °C + 273.15 o °C = (°F - 32) / 1.8 o °F = (1.8)(°C ) + 32
Metric System:
BIGGER than base unit Base Unit SMALLER than base unit
1 m = 10 dm
1 km = 1000 m
1 hm = 100 m
1 dam = 10 m
1 meter
1 liter
1 gram
1 m = 100 cm
1 m = 1000 mm
1 m = 10 6 µm
1 m = 10 9 nm
* The bigger unit always equals 1, then determine how many of the smaller units fit into 1 of those bigger units

Metric Conversions (the way to SHOW your work & units) o Convert 945 mL to dL

o Convert 0.54 km to nm
Density: o Density = mass
volume
Volume:

Most common units: L, mL, cm 3 o 1 mL = 1 cm 3 o 1 L = 1 dm 3

Below are some conversion factors used in the SI System which we will use in this class. kilo- = 1000
1 kg = 1000 g
1 km = 1000 m
1 kL = 1000 L centi- = 1/100
100 cm = 1 m milli- = 1/1000
1000 mg = 1 g
1000 mm = 1 m
1000 mL = 1 L
Other Conversions
1 mL = 1 cm 3
1 L = 1 dm 3
1 cm = 10 mm
Solve each of the following problems by showing work. Show the correct set-up and always use units.
1. Determine the number of mm in 1600 m.
2. Determine the number of m in 1600 mm.
3. Determine the number of mm in 14.3 cm.
4. Convert 2875 cm 3 to liters.
5. Convert 5.2 cm of magnesium (Mg) ribbon to mm of Mg ribbon.
6. Convert 0.049 kg sulfur (S) to g of S.

7. Convert 0.020 kg of tin (Sn) to mg of Sn.
8. Convert 150 mg of acetylsalicylic acid (aspirin) to g of aspirin.
9. Convert 2500 mL of hydrochloric acid (HCl) to L of HCl.
10. A metallurgist is making an alloy that consists of 325 g of chromium (Cr) and 2.5 kg of iron (Fe).
Find the total mass of the mixture in kg.
13. How many mL of water (H
2
O) will it take to fill a 2.00 L bottle that already contains 1.87 L of H
2
O?
14. Convert 150 cm of copper (Cu) wire into mm of Cu wire.
15. Convert 0.5 g of sodium (Na) to kg of Na.
16. The density of lead (Pb) is 11.34 g/cm 3 . Find this density of Pb in units of kg/dm 3 . **Challenge**

For each problem below, write the equations and show your work. Always use units and the appropriate number of sig. figs. Box in your final answer.
1. The density of silver (Ag) is 10.5 g/cm 3 . Find the mass of Ag that occupies 965 cm 3 of space.
2. A 2.75 kg sample of a substance occupies a volume of 250.0 cm 3 . Find its density in g/ cm 3 .
3. Under certain conditions, oxygen gas (O
2
) has a density of 0.00134 g/mL. Find the volume occupied by 250.0 g of O
2
under the same conditions.
4. Find the volume that 35.2 g of carbon tetrachloride (CCl
4
) will occupy if it has a density of 1.60 g/mL.
5. The density of ethanol is 0.789 g/mL at 2
0ºC. Find the mass of a sample of ethanol that has a volume of 150.0 mL at this temperature.
6. 30.0 g of each of the following acids are needed. Find the volume of each acid (in mL) that will contain the 30.0 g sample which is needed. a. Hydrochloric acid (HCl), density = 1.164 g/mL

b. Sulfuric acid (H
2
SO
4
), density = 1.834 g/mL c. Nitric acid (HNO
3
), density = 1.251 g/mL
7. A rectangular box of lead (Pb) measures 20.0 mm X 30.0 mm X 45.0 mm. If the density of Pb is
11.34 g/ cm 3 , calculate the mass of the block.
8. A cube of gold (Au) has a side length of 1.55 cm. If the sample is found to have a mass of 71.9 g, find the density of Au.
9. An irregularly shaped sample of aluminum (Al) is put on a balance and found to have a mass of
43.6 g. The student decides to use the water-displacement method to find the volume. The initial volume reading is 25.5 mL and, after the Al sample is added, the water level has risen
41.7 mL. Find the density of the Al sample in g/ cm 3 . (Remember: 1 mL= 1 cm 3 )
10. A gas has a mass of 3175 g and takes up enough space to fill a room that is 2.00 m X 2.00 m X
5.00 m. Find the density of the gas in g/mL.

Dimensional Analysis (D.A.):
 It’s all about converting & matching up units!

D.A. provid es a way to check your solution method by following the units or “dimensions” of the problem

When a problem is solved correctly, the unwanted units will cancel with one another.
This will leave behind only the desired units!
 Units are… o Multiplied together o Divided into one another o Or canceled completely
 The key is… o Finding the correct ___________________ _________________ o Setting up the relationships to cancel out the units you don’t want
> D.A. – Relationships as Ratios:

How many dozen are there in 48 eggs? o What are the relationships/conversions you needed to know? o Relationship: o If we write that relationship as a ratio… o How did you know if you should multiply or divide???
 D.A. will figure that out for you!!!
> D.A. – Problem Solving Steps:
1) Identify the unknown (what you are solving for).
2) Write down what is given or known.
3) Look for relationships between the known and unknown.
* Note: it may take more than one relationship to get from the known to the unknown*
4) Arrange the relationships into a series of ratios so that the given unit will cancel out and the desired unit will be left over.
5) Multiply numbers across the top of the expression and divide numbers on the bottom.

given unit desired unit = desired unit
given unit
> D.A. – Intro Example:

How many large pizzas will I need for a birthday party with 22 guests if I allow each person to eat 4 slices?
> D.A. – Four Practice Problems: Practice the following using dimensional analysis and sig figs :
1) How many decimeters are equal to 32.74 yards?
2) How many milliliters are in 2.35 gal of water?
>> Derived Units as Ratios:

All derived units can be set up as ratios for use in D.A. o Density Example:
1.35 g/mL =
3) What is the mass of gold, which has a density of 19.3 g/cm 3 and a volume of 2.0 in 3 ?
4) The speed of light is 3.0 x10 8 m/s. What is the speed of light in mi/hr (mph)?

As chemistry students, you have two goals with problems. First, get the correct answer. Second, be able to show others WHY your answer is correct. Dimensional analysis meets both of these goals.
Dimensional analysis is always a GIVEN value and one or more CONVERSION FACTORS that allow you to determine the DESIRED value.
Any mathematical fact can serve as a conversion factor. 1 hour = 60 minutes

1 hour
60 min
or
60 min
1 hour
A. Solve the following using dimensional analysis. Answers should be rounded to the the appropriate number of sig. figs! Remember that exact #s do NOT count towards sig. figs.
1. Convert 2.83 days into seconds.
2. Convert 7.72 years into days.
3. Convert 0.0035 weeks into seconds.
4. Convert 180 days into minutes.
5. Convert your age into seconds
B. Density is often used as a conversion factor between the mass and volume of a sample.
For problems 6 & 7, use the density of liquid mercury (13.6 g/mL) and D.A. to solve!
6. What is the volume of a 175 gram sample of mercury?
7. What is the mass, in grams, of 1.00 gallon of mercury?
[4 qts = 1 gal; 1 qt = 4 cups; 1 cup = 236.588 mL;]

8. When I carry in a 5-gallon container of water from my car, I always wonder its weight. On the web and found that 1 lb = 0.453542 kg and 1 qt = 0.946353 L. Knowing that the density of water is 1.0 g/mL, calculate its weight in pounds.
6)
7)
8)
5)
3)
2)
4)
1)
Make the following conversions using dimensional analysis and circle your answers reported with the appropriate number of significant figures.
Convert 0.054692 inches to feet
Convert 84.64 mph to km/s
Convert 4.75 decimeters to nanometers
Aluminum has a density of 2.693 g/mL. If you have an empty aluminum sheet with a mass of
0.000852 pounds, what is the volume of the sheet in liters? (1 lbs = 0.453592 kg)
Convert 90 centuries to weeks
Convert 27 months to fortnights (there are 14 days in a fortnight and ~30 days in a month)
Convert 0.09 miles to inches (there are 36 inches in a yard and 1760 yards in a mile)
Convert 4.66 centimeters to miles (there are 0.6 miles in a kilometer)

9) Convert 556 degrees Celsius to Kelvins (do not need to use dimensional analysis here)
10) Convert 25 Kelvins to degrees Celsius (do not need to use dimensional analysis here)
A. SI Units
What type of measurement is indicated by each of the following units? Choices are in the last column.
1) g/mL
2) s
3) km
4) g
5) cm 3
6) mm
7) mg
8) L
9) g/cm 3 density length mass time volume
B. Density
10) A small gold nugget has volume of 0.87 cm 3 . What is its mass if the density of gold is 19.3 g/cm 3 ?
11) What volume is occupied by 35.2 g of carbon tetrachloride if its density is 1.60 g/mL?
C. Unit Conversions - Perform the following metric conversions using dimensional analysis:
12) 25 kg  g
14) 0.36 mm   m
13) 9.3 mL  L
15) 24 cm  km
16) How many kilometers are there in 3.4 miles?
17) If a man’s mass is 180 pounds, find his mass in grams. (hint: 1 kg = 2.2 lbs)
18) How many kilograms is a 43.5-in 3 sample of silver if the density of silver is 10.5 g/cm 3 ?

19) How many liters are there in 13 cases of cola if each can is 12 ounces and each case contains 24 cans. (1 quart = 32 ounces)
1. SI units and metric conversions: match equivalent terms.
_____ __ 0°C a. 1000 m
_______ 1 km
_______ 100 mm
______ _ 77°F
_______ 2 cm
_____
__ 100°C
_______ 2000 mg
_______ 1000 ml
_______ 1 cm 3
_______ 0.01 L b. 373 K c. 1 dm 3 = 1 L *memorize d. 10 ml e. 0.10 kg f. 0.10 m g. 25°C h. 32°F
1. 200 mm j. 2 g
k. 1 ml
l. 0.02 m
m. 300 K
2. Metric Relationships: complete the following metric conversions. a. 1.0 x 10 3 mg________________ = _____________ kg b. 0.25 mm___________________ = _____________ pm c. 12.63 µg___________________ = _____________ g d. 1,039 ns___________________ = _____________ s

e. 1 dm 3 = _____________ L * should be memorized *
3. Dimensional analysis: complete the following conversions paying particular attention to units and significant figures. Show your work! a. A car is moving at a speed of 65.0 mph, calculate its speed in cm/s. b. The density of a grain of alcohol is 0.79 g/mL at 20°C. Calculate its density in pounds/gallon. (1 gallon = 3.785 L, 1 lb. = 453.59 g) c. d.
An atom of oxygen has a mass of 2.68 x 10 -23 g. How many oxygen atoms are in 10 pounds of oxygen? (1 kg = 2.2 lbs)
Bill Rogers won the 1979 Boston marathon (26.2 miles) in a time of 2 hrs: 9 min: 7 sec.
Calculate his speed in cm/min. (1 km = 0.62137 mi) e. The diameter of a hydrogen nucleus is 1 x 10 -13 pm and its mass is 1.67 x 10 -21 mg.
Calculate its density in g/ml.