1. Anything in black letters = write it in your notes (‘knowts’)
Chapter 3
Scientific Measurement
Anything in black letters = write it in your notes (‘knowts’)

2. Measurements without units are useless!
3.1 – Using & Expressing Measurements
Measurements without units are useless!
“I walked 5 today.”
“The speed of light is 186,000
“I weigh 890”
“20 of water”
All measurements need units!

3. The coefficient must be between 1 and 10, exponent must be an integer.
We will often work with really large or really small numbers in this class.
Standard Notation
Scientific Notation
872,000,000 grams
moles
= x 108 grams
= 5.6 x 10-6 moles
exponent
coefficient
6.02 x 1023
The coefficient must be between 1 and 10, exponent must be an integer.

4. Multiplication and Division
To multiply numbers written in scientific notation, multiply the coefficients and add the exponents.
(3 x 104) x (2 x 102)
= (3 x 2) x 104+2
= 6 x 106
(2.1 x 103) x (4.0 x 10–7)
= (2.1 x 4.0) x 103+(–7)
= 8.4 x 10–4

5. To divide numbers written in scientific notation, divide the coefficients and subtract the bottom exponent from the top exponent.
Coefficient needs to be between 1 and 10

6. Addition and Subtraction
When adding or subtracting in Sci. Not., the exponents must be the same.
Not the same, need to adjust one of the exponents
(5.4 x 103) + (8.0 x 102)
= (5.4 x 103) + (0.80 x 103)
= ( ) x 103
= 6.2 x 103

7. Example
Solve each problem and express the answer in scientific notation.
a. (8.0 x 10–2) x (7.0 x 10–5)
b. (7.1 x 10–2) + (5 x 10–3)

8. (8.0 x 10–2) x (7.0 x 10–5) = (8.0 x 7.0) x 10–2 + (–5) = 56 x 10–7a.
Multiply the coefficients and add the exponents.
(8.0 x 10–2) x (7.0 x 10–5)
= (8.0 x 7.0) x 10–2 + (–5)
= 56 x 10–7
= 5.6 x 10–6

9. b.
Rewrite one of the numbers so that the exponents match. Then add the coefficients
(7.1 x 10–2) + (5 x 10–3)
= (7.1 x 10–2) + (0.5 x 10–2)
= ( ) x 10–2
= 7.6 x 10–2

10. Accuracy -
closeness of a measurement to the actual or accepted value.
Precision -
closeness of repeated measurements to each other

11. Accuracy and Precision
Darts on a dartboard illustrate the difference between accuracy and precision.
Poor Accuracy, Poor Precision
Good Accuracy, Good Precision
Poor Accuracy, Good Precision
The closeness of a dart to the bull’s-eye corresponds to the degree of accuracy. The closeness of several darts to one another corresponds to the degree of precision.

12. Error
Suppose you measured the melting point of a compound to be 78°C
The actual melting point value (from reference books) is 76°C.
The error in your measurement would be 2°C.
Error = experimental value – accepted value
Error is how far off your measurement is from the actual or known value.

13. How far off you are in a measurement doesn’t tell you much.
For example, lets say you have $1,000,000 in your checking account. When you balance your checkbook at the end of the month, you find that you are off by $175; error = $175
Now, lets be more realistic, you have $225 in your checking account and after balancing you are off by $175!

14. Percent error compares the error to the size of the measurements.
In both cases, there is an error of $175.
But in the first, the error is such a small portion of the total that it doesn’t matter as much as the second.
So, instead of error, percent error is more valuable.
Percent error =
error
accepted value
100% x
Percent error compares the error to the size of the measurements.

16. ASSIGN: Chapter 3 Worksheet #1

17. 30.2°C In any measurement, the last digit is estimated
Significant Figures
In any measurement, the last digit is estimated
30.2°C
The 2 is estimated (uncertain) by the experimenter, another person may say 30.1 or 30.3

18. 9.3 mL
0.72 cm

19. Increasing Precision

20. The significant figures in a measurement include all of the digits that are known, plus the last digit that is estimated.
Numbers that are NOT significant are called placeholders.

21. HOLY SMOKES!! Rules for determining Significant Figures (p. 67)
1. Every nonzero digit in a reported measurement is assumed to be significant.
2. Zeros appearing between nonzero digits are significant.
3. Leftmost zeros appearing in front of nonzero digits are not significant. They act as placeholders. By writing the measurements in scientific notation, you can eliminate such placeholding zeros.
4. Zeros at the end of a number and to the right of a decimal point are always significant.
5. Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are not significant if they serve as placeholders to show the magnitude of the number.
5 (continued). If such zeros were known measured values, then they would be significant. Writing the value in scientific notation makes it clear that these zeros are significant.
6. There are two situations in which numbers have an unlimited number of significant figures. The first involves counting. A number that is counted is exact.
6 (continued). The second situation involves exactly defined quantities such as those found within a system of measurement.
HOLY SMOKES!!

22. A shorter method for determining which numbers are significant in a measurement.
All nonzero numbers are significant.
Zeros are also significant if they are NOT placeholder zeros.
Counted and exact numbers have an unlimited number of sig figs.
The Tischer Method!™
A placeholder is a zero that ‘holds place’; it is only there to show how big or small a number is.

24. Underline the zeros that are placeholders
A placeholder is a zero that ‘holds place’; it is only there to show how big or small a number is.
Zeros to the right of a number & after the decimal are more than placeholders, they are part of the measurement and are significant.

25. How many significant digits are in the following measurements?
a) grams b) mL
c) cm d) 4.00 lbs
e) m f) cm
g) 100 grams h) 1.00 x 102 grams
i) 11 cars j) 2 molecules
All nonzero numbers are significant.
Zeros are also significant if they are NOT placeholders.
Counted and exact numbers have an unlimited number of sig. figs.

26. Another Shorter Method
“Box and Dot” Method for Counting Sig Figs
1. Draw a box around all digits from the 1st nonzero digit on left to last nonzero digit on the right.
2. If a dot is present, draw a box around any trailing zeros.
3. Any boxed digit is significant.
Another Shorter Method
SOURCE: JCE Vol 86 No 8 (Aug ‘09) W. Kirk Stephenson

27. A answer can’t be more accurate than the measurements it was calculated from

28. Rules for Add/Subtracting Sig Figs
The answer to an +/- calculation should be rounded to the same number of decimal places as the measurement with the least number of decimal places.
3.2 cm
37.10 g

29. Rules for Mult/Division Sig Figs
The answer to a x/÷ calculation should be rounded to the same number of sig figs as the measurement with the least number of sig figs.
3.8 cm2

30. ASSIGN: Chapter 3 Worksheet #2
Always round your final answer off to the correct number of significant digits.
ASSIGN: Chapter 3 Worksheet #2

31. 3.2 – Units of Measurement SI – International System of Units
SI Base Units (page 74)
Quantity
SI base unit
Symbol
Length
meter m
Mass
kilogram kg
Temperature
kelvin K
Time
second s
Amount of substance
mole
mol
Luminous intensity
candela cd
Electric current
ampere A
We will use all of these in this class
How is Mass different from Amount of Substance?

32. Commonly Used Metric Prefixes (page 75)
Symbol
Meaning
Factor
mega M
1 million times larger than the unit it precedes
106
kilo k
1000 times larger than the unit it precedes
103
deci d
10 times smaller than the unit it precedes
10-1
centi c
100 times smaller than the unit it precedes
10-2
milli m
1000 times smaller than the unit it precedes
10-3
micro μ
1 million times smaller than the unit it precedes
10-6
nano n
1 billion times smaller than the unit it precedes
10-9
pico p
1 trillion times smaller than the unit it precedes
10-12

33. Volume - Amount of space occupied by an object (remember?)
Normal units used for volume:
Solids – m3 or cm3
Liquids & Gases – liters (L) or milliliters (mL)
1 L = 1000 mL 1 mL = 1 cm3
The volume of a material changes with temperature, especially for gases.

34. Mass - Weight - Measure of inertia (remember?)
Force of gravity on a mass; measured in pounds (lbs) or Newtons.
Weight can change with location, mass does not

35. 1 cal = 4.184 J Energy – Ability to do work or produce heat.
Normal units used for energy:
SI – joule (J)
non-SI – calorie (cal)
1 cal = J
How many joules are in a kilojoule?
How many calories are in a kilocalorie?

36. Temperature –
measure of how cold or hot an object is.

37. K = °C + 273 yucky! Temperature –
measure of the average kinetic energy of molecules.
Normal units used for temp:
SI – kelvin (K)
non-SI – celsius (°C) or Fahrenheit (°F)
yucky!
K = °C + 273

38. Celsius
Kelvin
100
divisions
100°C
Boiling point
of water K
0°C
Freezing point K

39. Density is an intensive property
mass
volume
Density =
Density is an intensive property
Normal units for density:
g/cm3, g/mL, g/L

40. Densities of Some Common Materials
Solids and Liquids
Gases
Material
Density at 20°C (g/cm3)
Density at 20°C (g/L)
Gold
19.3
Chlorine
2.95
Mercury
13.6
Carbon dioxide
1.83
Lead
11.3
Argon
1.66
Aluminum
2.70
Oxygen
1.33
Table sugar
1.59
Air
1.20
Corn syrup
1.35–1.38
Nitrogen
1.17
Water (4°C)
1.000
Neon
0.84
Corn oil
0.922
Ammonia
0.718
Ice (0°C)
0.917
Methane
0.665
Ethanol
0.789
Helium
0.166
Gasoline
0.66–0.69
Hydrogen
0.084

41. ASSIGN:
Read 3.2
Lesson Check 3.2; #23-35 (page 82)

42. 4.184 Joules = _______ calorie
3.3 – Solving Conversion Problems
12 inches = ______ foot
1 minute = _____ seconds
10 cents = _______ dime
24 hours = ______ day
1 km = ________meters
4.184 Joules = _______ calorie
Fill in the blanks…
These can all be used as conversion factors

43. Conversion Factors
When two measurements are equal, they can be used as conversions between units.
1000 g
1 kg
and
Conversion factors
1 mile
5280 feet
and
60 min
1 hour

44. Method used to convert measurements to other units.
Dimensional Analysis
Method used to convert measurements to other units.
Start with given information.
Use conversion factors to cancel units until desired unit is left.

45. How many seconds are in 8 hours?
Example 1
How many seconds are in 8 hours?
Start with given information.
Use conversion factors to cancel units until desired unit is left.
60 min = 1 hr; 60 sec = 1 min
Multiply across the top,
divide along the bottom of the conversion factors.

46. How many km are in 25 miles? Example 2 Start with given information.
Use conversion factors to cancel units until desired unit is left.
1.6 km = 1 mile
Multiply across the top,
divide along the bottom of the conversion factors.

47. 5.26 mumu = 8 nunu; 1.76 nunu = 12.35 fufu; 0.826 fufu = 1035 bubu.
Example 3 – TRY IT!
5.26 mumu = 8 nunu;
1.76 nunu = fufu;
0.826 fufu = 1035 bubu.
1. How many mumus are in 10 bubus?

48. 5.26 mumu = 8 nunu; 1.76 nunu = 12.35 fufu; 0.826 fufu = 1035 bubu.
Example 4 – TRY IT!
5.26 mumu = 8 nunu;
1.76 nunu = fufu;
0.826 fufu = 1035 bubu.
2. How many fufus are in 26 mumus?

49. A student converted 10.1 feet as follows:
How many significant digits should the answer have?
Why not 1?

50. ASSIGN:
Chapter 3 Worksheet 3

51. Conversion Factor Quiz Show your WORK for credit.
1 horsepower = W
2.54 cm = 1 inch
LEFT: 1. Convert 6.5 horsepower into watts
RIGHT: 1. Convert 100 watts into horsepower
LEFT: 2. How many cm are in 12 miles?
RIGHT: 2. How many cm are in 20 miles