Chapter 5
Measurements and Calculations
Title: Oct 1­1:58 PM (1 of 24)
Scientific Notations
When you work with chemistry concepts, you will often find that extremely large
numbers and extremely small numbers are used. For example, the speed of light is
approximately 30,000,000,000 cm/sec. Numbers expressed in this way are
awkward and have little meaning to us. Numbers like these cannot be quickly
comprehended at first sight. Therefore, a more convenient way to express such
numbers is as exponential numbers.
Exponential numbers are numbers expressed as multiples or powers of ten.
Exponential numbers are a form of what is called ___________________.
The following illustrates how common numbers may be expressed as exponential
numbers.
10 = _______
100 = _______
1000 = _______
0.1 = ________
0.01 = _______
0.001 = _______
*There is a rule for correct decimal placement in an exponential number. When
writing in scientific notation, the decimal point should be placed in the ______
position. This means it is placed between the first 2 digits!
Title: Oct 1­2:07 PM (2 of 24)
Converting Numbers to Scientific Notation
Coefficient
1.7 X 1014
Exponent
*Numbers less than one have a NEGATIVE exponent
Ex: 0.000647 6.47 X 10­4
*Numbers greater than one have a POSITIVE exponent
Ex: 175000 1.75 X 105
Complete the following problems by writing them in either exponential form
or regular form.
1. 190,000
6. 1.986 x10^5
2. 528
7. 1.986 x 10^8
3. 4,400,000
8. 1.75 x10^7
4. 9700
9. 3.33 x 10^4
5. 49
10. 2.5 x 10^1
What do we do with numbers that are smaller than 1? Complete the following
problems by writing them in either exponential form or regular form.
1. 0.056
6. 9.28 x10^-8
2. 0.113
7. 1.411 x 10^-3
3. 0.00000035
8. 6.275 x 10^-6
4. 0.00077
9. 2.79 x 10^-4
5. 0.0000512
10. 1.3 x 10^-1
Title: Oct 1­2:16 PM (3 of 24)
Adding or Subtracting Using Scientific Notation
Carry out the following operations
1. (1.62 x 10^-3) + (3.4 x 10^2)
2. (1.75 x10-1) - (4.6 x 10^-2)
3. (1.56 x 10^12) + (8.25 x 10^9)
4. (8.65 x 10^25) - (1.25 x 10^23)
Title: Oct 1­2:33 PM (4 of 24)
Multiplication and Division Using Scientific Notation
Carry out the following operations
1. (1.51 x 103) x (3.2 x 10­2)
2. (6.02 x 1023) x (2.0 x 102)
3. (6.02 x 1023) / (1.2)
4. (3.456 X10-5) / (2.15x 108)
Title: Oct 1­3:01 PM (5 of 24)
The SI Measurement System
In science, we use a system of measurement called the _______________. It was first introduced in France more than _____________ years ago. SI units are used by scientists in all nations, including the United States. This system has a small number of base units from which all other necessary units are derived.
Title: Oct 1­3:06 PM (6 of 24)
1. Which metric unit and prefix would be most convenient to measure each of the following?
a. the thickness of a dime ________________
b. the mass of gasoline in a gallon___________
c. the mass of a cold virus ________________
d. the diameter of a human hair ____________
e. the time necessary to blink your eye _______
2. Do the following metric conversions
a. 234 cm = _________meters
234 cm 1 m 100 cm
15.2 L 1000mL
1L
b. 15.2 liters = ________ milliliters
c. 125 ml = __________ liters
125 mL 1 L
1000 mL
d. 124 grams = ___________ kilograms
e. 256 mm = _________ km
f. 1.3 m = __________ mm
g. 15 mg = _________ g
h. 25 cm = ________km
i. 1.8 meters = ________mm
123 g 1 kg
1000 g
256 mm 1 m 1 km
1000 mm 1000m
1.3 m 1000 mm
1 m
15 mg 1 g
1000 mg
25 cm 1 m
100 cm
1 km
1000 m
1.8 m 1000 mm
1 m
Title: Oct 1­3:11 PM (7 of 24)
3. Solve the following problems
a. An antacid tablet contains 168 mg of the active ingredient
ranitidine hydrochloride. How many grams of the compound are in the table?
168 mg
1 g
1000 mg
b. There are 1.609 km in 1.00 mile. Determine the number of centimeters in one mile.
1 mi 1. 609 km 1000 m 100 cm
1 1 mi
1 km
1 m
c. A paper clip is 3.2 cm long. What is its length in millimeters?
3.2 cm
10 mm
1 cm
d. The average person in the United States uses 350 liters of water daily. Convert this
volume to milliliters.
350 l 1000 ml
1 l
e. A desk is 2 meters long. How many centimeters long is it?
2 m 100 cm
1 1m
f. A car weights 1525 kilograms. How many milligrams would it weigh?
1525 kg 1000 g
1 1 kg
Title: Oct 1­3:22 PM (8 of 24)
1000 mg
1 g
Factor Label Method
Notice that all of the problems you have completed so far have units as a part of
the answer. Numbers without units are meaningless. Therefore, we must be
able to handle both numbers and their units with efficiency. There are several
rules you should use when solving problems with units. They are:
1. Only quantities with the same ____________ can be added or
subtracted.
2. When quantities are multiplied or divided, their units are also
_____________ or _______________.
3. The units that do not ___________________ in a problem
become the units in the answer.
Example Problem
Convert 4 hr to seconds.
Necessary Conversions!!!
1 hr = 60 min
1 min = 60 s
4 hr
1
Notice that all of the units except seconds cancel out. If the units cancel out
correctly, you know you have set up the problem correctly.
Let‛s try another example.
Calculate the number of seconds there are in one week.
60 s = 1 min 60 min = 1 hr
24 hr = 1 day 7 days = 1 week
Necessary Conversions !!!
1 week 1
Solve the following problems using the methods discussed in class. Remember
for full credit, you must show your work!!
Title: Oct 2­7:22 PM (9 of 24)
Conversion Table
1 inch = 2.54 cm
1 mi = 5,280 ft
1 hour = 3600 sec
1 ft = 12 in
1 day = 24 hours
1 fl oz = 29.6 mL
1 mi = 1.6 km
1 L = 1000 mL
1 L = 1.06 qt
1 lb = 454 g
1. Find the number of centimeters in 5 inches.
2. Convert 55 mi/hr to km/min.
3. Find the number of feet in 54.2 miles.
4. Two liters are how many milliliters?
5. Three feet are how many centimeters? How many miles?
6. 7.8 pounds are equal to how many grams?
7. Convert 987 mL to fluid oz, liters, and quarts.
8. 7,895,000 seconds are equal to how many hours?
9. Convert 84 kilometers to miles, feet, and inches.
10. The school year has 177 school days, how many minutes is that?
Extra Credit
Here is some unusual data: Two warts contain 1 querk, 3 querks make 1 gag, 5 gags
compose 6 nerfs, and 4 nergs make 5 wigs. How many warts are there in a wig? You
must show your work.
Title: Oct 2­8:17 PM (10 of 24)
Section 5.4 Uncertainty in Measurement
A. Why are measurements uncertain?
*Measuring instruments are never flawless
*Measuring always involves some estimation
B. Tools for Measurement
*Electronic Balance
­Displays digital amount
­Last digit is estimated by the machine and therefore flickers
­Be sure to include UNITS!
Estimated Digit
*Estimating with Scales
­Example: Graduated Cylinder
*Measure from the bottom of the meniscus
*Includes all the lines you can read and include one estimate digit!
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*Box the Uncertainty (Estimated) Digit
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5.5 Significant Figures
Measurements are an integral part of most chemical experimentation. However, the numerical measurements that result have some inherent _________________. This _________________ is a result of the measurement device as well as the fact that a human being makes the measurement. No measurement is absolutely __________________.
When you use a piece of laboratory equipment, read and record the measurement to one decimal place beyond the smallest marking on the piece of equipment. Guidelines for Determining Significant Digits
1. All digits recorded from a laboratory measurement are called significant digits
Significant Digits: All the certain digits and one estimated digit
2. All non­zero digits are considered significant
3. A middle zero is always significant
Ex: 303 has 3 sig figs
4. A leading zero is never significant. It is only a placeholder; not part of the actual measurement.
Ex: 0.0123 kg the first 2 zeros are not significant. The number has 3 sig figs
5. A trailing zero is significant when it is to the right of a decimal point.
Ex: 23.20 mL (the number has 4 sig figs) The zero to the right of the decimal
Ex: 150 g the number has 2 sig figs. The zero is to the left of the decimal and not significant
*SPECIAL NOTES (ADD to your blank pages)
Rules for Significant Digits:
P
(Pacific)
1. All non­zero numbers are significant
2. Any zeros sandwiched between 2 non­zero digits are significant
3. Atlantic­Pacific Rule
a. Decimal Present count from the Pacific side @ first non­zero digit
b. Decimal Absent count from the Atlantic side @ first non­zero digit
Title: Oct 7­11:27 PM (13 of 24)
A
(Atlantic)
How many significant figures are in each of the following?
1. 451,000 m
2. 6.02 X 1023 mol
3. 0.0540 mL
4. 0.0065 g
5. 4046
6. 203,034,000
7. 10
8. 200
9. 3000
10. 1.0
Using Significant Figures in Calculations
Addition and Subtraction
* Look at the decimal point!
­The number of decimal places in the answer should be the same as in the measured quantity with the smallest number of decimal places.
Ex: 12. 015
+ 3. 41
0.003
+ 1
4.1568
+10.5
Answer the following problems using the correct number of significant figures
1. 16.27 + 0.463 + 32.1
2. 42.05 ­ 3.6
3. 1.23 + 2.345 + 68.9
4. 66.5 ­ 2.36
Title: Oct 7­11:53 PM (14 of 24)
Multiplication and Division
*The number of significant figures in the answer should be the same as in the measured quantity with the smallest number of signficant figures
Examples: 12.334 / 100 = Practice
1. 13.36 X 12.6
2. 13.36 / 0.0468
3. 1.2030 X 2.5698
4. 1.078 / 3.290
5. (13.36 + 0.045) x 11.6
6. (12.21 + 0.321) / 1.02
Title: Oct 8­12:02 AM (15 of 24)
14.5 / 12.111 = Answers to Practice Quiz
5651 (2) 5700
15.0501 (4) 15.05
1650. (1) 2000 or 2 X 103
0.00501 (2) 0.0050
8.99546 (3) 9.00
3000 (3) 3.00 X 103
0.0001050 (4)
1.00 (3)
5000 (1)
10 (1)
1.02 (3)
5000. (4)
56.12/12 = 4.7
17.09 X 0.005 = 0.09
0.005/170 = 3 X 10­5
0.04400 X 100.5 = 4.422
5.6661 + 11.32 = 16.99
10.53 ­ 9.86 = 0.67
100. ­ 9.54 = 90.
16.00 + 0.059 = 16.06
Write following numbers in scientific notation.
0.0000000563 5.63 X 10­8
602000000 = 6.02 X 108
13470000 1.347 X 107
0.000456 = 4.56 X 10­4
Write the following numbers in standard notation.
4.5 x 104 45000
8.9 x 108 890 000 000
5.60 x 10­1 0.560
5.000 x 103 5000
Convert the following using dimensional analysis.
22.0 km = 220 000 dm
7620 mg = 0.00762 kg
22.0 km 10000 dm
1 1 km
57 mm = 5.70 cm
4.0 cg = 40. mg
57 mm 1 cm
10 mm
79.3 mm = 0.260 ft
Title: Oct 9­12:41 PM (16 of 24)
43 miles = 75680 yards
Density
The density of a substance relates the ___________ of the substance to its ___________.
Density is expressed mathematically as
Density is usually expressed in the units _____________ or __________.
Let‛s try some example problems
Find the density of 25.0 cm3 of a metal if it has a mass of 65.0 grams.
The density of iron is 7.5 g / mL. What is the mass of a cube that has a volme of 8.9 mL?
Solve the following problems
1. A block of 56.0 cubic centimeters weighs 256.0 g. What is the density of the block?
2. 88.0 g of a liquid occupies 85 mL of space. What is the density of the liquid?
3. The density of concentrated sulfuric acid is 1.84 g/mL. What is the mass of 256 mL of this
acid?
4. The density of iron is 7.5 g/cm3. What is the mass of a cube of iron that measures
7 cm on each side?
Title: Oct 8­3:16 PM (17 of 24)
Percents and Percent Error
A. Express as a Percent (%)
1. Convert fraction to a decimal
2. Multiply decimal by 100
Example: 3/4 = 0.75 x 100 = 75%
B. Percent Error
1. Formula: Accepted ­ Experimental
x 100
Accepted
Absolute Value
2. Experimental = You measure during an experiment
3. Accepted = Value you are supposed to get (often given to you)
Title: Oct 9­9:39 PM (18 of 24)
Temperature
A. Temperature Scales
1. Celsius Scale: Freezing point of Water = 0 0 C
Boiling Point of Water = 1000 C
2. Kelvin Scale: Water Boils (373 K) *No Degrees
Water Freezes (273 K)
*Absolute Zero
B. Conversions
1. Converting between the Kevin and Celsius
0C = K ­ 273
Examples: 276 K = _______ 0C
1000C = _______ K
Title: Oct 9­9:39 PM (19 of 24)
K = 0C + 273
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0.843 g/ml
Title: Oct 12­7:08 AM (24 of 24)
Attachments
Sig Fig tutorial
Sig Fig tutorial II