1. Scientific measurement

2. Number vs. Quantity UNITS MATTER!! Quantity - number + unit
Courtesy Christy Johannesson

3. 2.1 Types of measurement Quantitative- use numbers to describe
Qualitative- use description without numbers
4 feet
extra large
Hot
100ºF

4. 2.1 Scientists prefer.. Quantitative - easy to check
Easy to agree upon, no personal bias
The measuring instrument limits how good the measurement is.

5. 2.2 How good are the measurements?
Scientists use two word to describe how good the measurements are
Accuracy- how close the measurement is to the actual value
Precision- how well can the measurement be repeated

6. Accuracy vs. Precision Systematic errors: reduce accuracy
Scientists repeat experiments many times to increase their accuracy.
Good accuracy
Good precision
Poor accuracy
Good precision
Poor accuracy
Poor precision
Systematic errors:
reduce accuracy
Random errors:
reduce precision
(instrument)
(person)

7. 2.2 Differences
Accuracy can be true of an individual measurement or the average of several
Precision requires several measurements before anything can be said about it
examples

8. Let’s use a golf anaolgy

9. Accurate? No
Precise?
Yes 10

10. Accurate?
Yes
Precise?
Yes 12

11. Precise? No
Accurate?
Maybe? 13

12. Accurate?
Yes
Precise?
We cant say! 18

13. REVIEW: Accuracy vs. Precision
Accuracy - how close a measurement is to the accepted value
Precision - how close a series of measurements are to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT
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14. 2.3 Scientific Notation 65,000 kg  6.5 × 104 kg
Converting into Scientific Notation:
Move decimal until there’s 1 digit to its left. Places moved = exponent.
Large # (>1)  positive exponent Small # (<1)  negative exponent
Only include sig figs.
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15. 2.3 Converting Numbers to Scientific Notation
2.205 x 10-5 1 2 3 4 5
In scientific notation, a number is separated into two parts.
The first part is a number between 1 and 10.
The second part is a power of ten.

16. Form: (# from 1 to 9.999) x 10exponent 800 = 8 x 10 x 10 = 8 x = x 10 x 10 x 10 = x = 1.4 / 10 / 10 / 10 = 1.4 x 10-3

17. 2.3 Scientific Notation Practice Problems
1. 2,400,000 g kg 3. 7  10-5 km  104 mm
2.4  106 g
2.56  10-3 kg km
62,000 mm
Courtesy Christy Johannesson

18. Using the Exponent Key on a Calculator

19. EE or EXP means “times 10 to the…”
How to type out 6.02 x 1023:
How to type out 6.02 x 1023: 6 EE . 3 2 6 EE . 3 2
Don’t do it like this…
WRONG! 6
y x . 3 2
WRONG!
…or like this… x 1 6 . 2 EE 3
…or like this:
TOO MUCH WORK.
y x 3 2 x 1 6 .

20. Example:
1.2 x 105
2.8 x 1013 = 1 . 2 EE 5 3 8
Type this calculation in like this:
–09
Calculator gives…
E–09
or…
This is NOT written…
4.3–9
4.3 x 10–9
But instead is written…

21. Scientific Notation Type on your calculator: EXP EE EXP EE EXE 5.44 7
Calculating with Scientific Notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
Type on your calculator:
EXP EE
EXP EE
ENTER
EXE
5.44 7
8.1 ÷ 4 =
= 670 g/mol
= 6.7 × 102 g/mol
Courtesy Christy Johannesson

22. How to Use a Scientific Calculator
Divide: (5.44 x 107) / (8.1 x 104)
5.44
8.1 00 07 00 04
How to enter this on a calculator: . EE . EE
ENTER OR .
EXP .
EXP =
rounded to 6.7 x 102
Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 52

23. 2.3 How reliable are Measurements?
How do you make a measurement?
With most measuring devices, you should be able to estimate to one decimal place more than the smallest division on the device.
The smallest division is a _____ of a centimeter, so you can guess to the _____________ (or ___ decimal places like 1.24).
tenth
hundredth 2

24. Using A Ruler
= cm
= cm
= 1.5 cm

25. 1 2 3
1 =
5.73
2 =
3.0
3 =
.35

26. 2.3 Significant Figures 1.19 cm Indicate precision of a measurement.
Recording Sig. Figs.
Sig. figs. in a measurement include the known digits plus a final estimated digit
1.19 cm
Centimeters 1 2 3 4 5
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27. 2.3 Measurement – Significant Figures
All of the known digits plus the estimated digit are significant – they are not placeholders.
When we measured the volume of cylinder 1 on the last slide we got:
5.73 mL
known estimated
This would mean 3 significant figures.

28. 100
200
300
100
200
300
120 mL
120 mL

29. Significant Figures
100
200
300
100
200
300
What is the smallest mark on a graduated cylinder that measures cm?
242 mL?
240 mL?
Here there’s a problem… does the zero count or not?

30. 2.3 Measurement – Significant Figures
Significant Figure Rules
Every nonzero is significant.
123.2 g 4 sig figs
Zeros between nonzero digits are significant.
1004 m 4 sig figs
Zeros to left of nonzero are NOT significant.
0.01 g 1 sig fig
Zeros to the right of a nonzero number if there is no decimal point are NOT significant
1200 g 2 sig figs

31. Sig figs. How many sig figs in the following measurements? 458 g

32. Significant Figures Counting Sig Figs REVIEW Count all numbers EXCEPT:
Leading zeros
Trailing zeros without a decimal point -- 2,500
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33. Significant Figures Practice
Counting Sig. Figs. Examples
4 sig figs
3 sig figs
3. 5,280
3. 5,280
3 sig figs
2 sig figs
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34. Sig Figs.
405.0 g
4050 g
0.450 g g g
Next we learn the rules for calculations

35. Rounding rules Look at the number behind the one you’re rounding.
If it is 0 to 4 don’t change it
If it is 5 to 9 make it one bigger
Round to four sig figs
to three sig figs
to two sig figs
to one sig fig

36. Rounding Practice Round the following to 3 significant figuresm
527,254 g
4.998 mL
959,600 m

37. Scientific Notation Quiz
Write in Standard form
x x 103
Write in Scientific Notation
3) g 4) m
Calculate~ Answers need to be in scientific notation!
5. (6.02 X 1023) X (9.54 x 10-13)
6. (5.23 X 10-21) / (1.23 X 1023)

38. 2.5 Significant Figures in Calculations
An answer can’t have more significance than the measurements upon which it is based.
YOUR ANSWER IS ONLY AS GOOD AS YOUR WORST MEASUREMENT!

39. Significant Figures (13.91g/cm3)(23.3cm3) = 324.103g 324 g
Calculating with Sig Figs
Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.
(13.91g/cm3)(23.3cm3) = g
4 SF
3 SF
3 SF
324 g
Courtesy Christy Johannesson

40. Multiplication and Division
Same rules for division
Practice
4.5 / 6.245
4.5 x 6.245
x .043
3.876 / 1983
16547 / 714

41. Significant Figures 224 g + 130 g 354 g 224 g + 130 g 354 g 3.75 mL
Calculating with Sig Figs (con’t)
Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.
224 g
+ 130 g
354 g
224 g
+ 130 g
354 g
3.75 mL mL
7.85 mL
3.75 mL mL
7.85 mL
 350 g
 7.9 mL
Courtesy Christy Johannesson

42. For example
27.93
6.4 +
First line up the decimal places
27.93
6.4 +
27.93
6.4
Then do the adding
Find the estimated numbers in the problem
34.33
This answer must be rounded to the tenths place

43. Significant Figures 2. 18.9 g - 0.84 g 18.06 g Practice Problems
1. (15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= g/mL
 2.4 g/mL
2 SF g g
 18.1 g
18.06 g
Courtesy Christy Johannesson

44. Problems 500 is only 1 significant figure
If it really has two, how can I write it?
A zero at the end only counts after the decimal place
Scientific notation
5.0 x 102
Now the zero counts.

45. Practice
x x x x 10-3

46. Significant Figures Calculating with Sig Figs (con’t)
Exact Numbers do not limit the # of sig figs in the answer.
Counting numbers: 12 students
Exact conversions: 1 m = 100 cm
“1” in any conversion: 1 in = 2.54 cm
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47. 2.5 Significant Figures in Calculations REVIEW
Addition Subtraction
Round your answer to the same number of decimal places as your least significant number.
Think of it as the leftmost uncertainty. m m m m
540 m

48. 2.5 Significant Figures in Calculations REVIEW
Multiplication and Division
Round answer to the same number of significant digits as the measurement with the least number of significant digits. m
× m 5 3 m2
2860 m2

49. 2.6 Units of Measurement – Metric
2. Metric – Developed in France in 1790.
Simple base units
Interchangeable prefixes
Decimal (base 10) system

50. Metric Prefixes Prefix Symbol Meaning kilo- k hecto- h deca- da deci-
centi- c
milli- m
1 km = m
1 hm = 100 m
1 dam = 10 m
10 dm = 1 m
100 cm = 1 m
1000 mm = 1 m

51. 2.1 Units of Measurement – SI Base Units
Quantity
Unit
Symbol
Length
meter m
Mass
kilogram kg
Time
second s
Temperature
kelvin K
Amount of Substance
mole
mol
Electrical current
ampere A
Luminous intensity
candela cd

52. No Cussing! Inch Mile Foot Pint Yard Acre Metric
The following 4-Letter
words are forbidden here:
Inch Mile
Foot Pint
Yard Acre
And we never swear the BIG F (useoC)
Please keep it clean and
Metric

53. Metric Conversions
kilo hecto deca base unit deci centi milli-
(k) (h) (da) (d) (c) (m)
Meter (m)
Liter (L)
Gram (g)
Second (s)
/ / /1000
To convert from 1 prefix to another, just move the decimal to the left or right that many places!

54. 5000 cg How many centigrams (cg) are in 5dag?1 2 3
kilo hecto deca base unit deci centi milli-
(k) (h) (da) (d) (c) (m)
Meter (m)
Liter (L)
Gram (g)
Second (s)
How many centigrams (cg) are in 5dag?
Just move the decimal ___ places to the ________! 5 3
right
5000 cg

55. .012 km 1 2 3 left How many kilometers (km) are in 12 meters m?
kilo hecto deca base unit deci centi milli-
(k) (h) (da) (d) (c) (m)
Meter (m)
Liter (L)
Gram (g)
Second (s)
How many kilometers (km) are in 12 meters m?
Just move the decimal ___ places to the ________!
1 2 3
left
.012 km

56. Volume calculated by multiplying L x W x H
Liter the volume of a cube 1 dm (10 cm) on a side
so 1 L = 10 cm x 10 cm x 10 cm
1 L = 1000 cm3
1/1000 L = 1 cm3
1 mL = 1 cm3

57. Measuring Volume: Tank of Water
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 143

58. Person Submerged in Water
Archimedes Principle: water displacement method to find the volume of an irregularly shaped object.
The volume the water level increased is equal to the volume of the submerged object.
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 143

59. Mass 1 kg = 2.5 lbs 1 g = 1 paper clip
1 mg = 10 grains of salt or 2 drops of water.

60. Density M V
D = M
M = D x V
ass D V M D
V =
ensity
olume

61. Density of Some Common Substances
Substance Density
(g / cm3)
Air *
Lithium
Ice
Water
Aluminum
Iron
Lead
Gold
*at 0oC and 1 atm pressure

62. Consider Equal Volumes
Mass
Density =
Volume
Equal volumes…
…but unequal masses
The more massive object
(the gold cube) has the
_________ density.
Question: Which weighs more a ton of feathers or a ton of bricks?
(They weigh the same)
Question: Which occupies a larger volume; a ton of feathers or a ton of bricks?
(the feathers will occupy a larger volume)
GREATER
aluminum
gold
Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 71

63. Consider Equal Masses Equal masses… …but unequal volumes.
The object with the
larger volume
(aluminum cube) has
the smaller density.
gold
aluminum
Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 71

64. Density
An object has a volume of 825 cm3 and a density of g/cm3. Find its mass.
GIVEN:
V = 825 cm3
D = 13.6 g/cm3
M = ?
WORK:
M = DV
M = (13.6 g/cm3)(825cm3)
M = 11,200 g
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65. Density
A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?
GIVEN:
D = 0.87 g/mL
V = ?
M = 25 g
WORK:
V = M D
V = g
0.87 g/mL
V = 29 mL
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66. 2.12 Temperature
Heat – type of energy transferred because of a difference in temperature.
Can’t be measured directly
Temperature – measure of the average kinetic energy of the particles in a sample of matter.
Determines the direction of heat transfer

67. 2.12 Temperature What does your body sense? temperature or heat
What contains more heat?
a glass of boiling water or an iceberg
What does your body sense?
temperature or heat

68. 2.12 Temperature Scales Celsius (C) – based on water
Fahrenheit (F) – zero based on equal mix of snow and ammonium chloride.
32F = freezing point of water
212F = boiling point of water
Celsius (C) – based on water
0C = freezing point of water
100C = boiling point of water

69. 2.12 Temperature Scales 0 K = all particle motion stops
Kelvin (K) - only temperature scales that is proportional to the speed of the particles.
0 K = all particle motion stops
273 K = freezing point of water
373 K = boiling point of water

70. 2.12 Temperature Conversion
T(K) = t(C) + 273
What is 25C (room temp.) in kelvin?
T(K) = 25C = 298 K
t(C) = T(K) – 273

71. Accuracy is very important when making measurements in the lab.
In order to evaluate the accuracy of a measurement, you must be able to compare the experimental value to the accepted value.
Accepted value = the true or correct value based on reliable references
Experimental value = the measured value determined in the experiment in the lab.

72. Percent Error
Indicates accuracy of a measurement expressed as a percentage
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73. Percent Error % error = 2.94 %
A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.
% error = 2.94 %
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