Standards of measurement involve using a measuring tool to compare some dimension of an object to a standard unit. For example, in the past the king's foot was used as the standard for length. Some problems with using this standard are that feet can vary in size between different kings and between individuals, making measurements inconsistent.

1. Standards of MeasurementStandards of Measurement
Using a measuring tool to compare some dimension ofUsing a measuring tool to compare some dimension of
an object to a standard.an object to a standard.
For example, at one time theFor example, at one time the
standard for length was thestandard for length was the
king’s foot. What are someking’s foot. What are some
problems with this standard?problems with this standard?

2. WHO CARES ABOUT MEASUREMENT?!
SCENARIOS:
1. Your friends ask you to go somewhere…
2.You want to go somewhere with your car…
3. You’re sick…
4.You’re hungry…
5.Buying a new outfit?
6.The sports field…
7.You start school at 7:45am but you’re leaving from
your friends house…
8.A tree falls on the road… can you lift it?
9.You’re vacationing and your plane must take off…

3. UNITS OF MEASUREMENTUNITS OF MEASUREMENT
Use SI units — based on the metric
system
Length
Mass
Volume
Time
Temperature

4. Types of Observations andTypes of Observations and
MeasurementsMeasurements
QUALITATIVEQUALITATIVE——changes in color andchanges in color and
physical state.physical state.
QUANTITATIVE MEASUREMENTSQUANTITATIVE MEASUREMENTS
------involveinvolve numbersnumbers
◦ UseUse SI unitsSI units — based on the— based on the
metric systemmetric system

5. Stating a MeasurementStating a Measurement
In every measurement there is aIn every measurement there is a
♦NumberNumber followed by a…followed by a…
♦ UnitUnit from a measuring devicefrom a measuring device
The number should also be asThe number should also be as preciseprecise as theas the
measurement!measurement!

6. Some Tools for MeasurementSome Tools for Measurement
Which tool(s)Which tool(s)
would you use towould you use to
measure:measure:
A.A. temperaturetemperature
B.B. volumevolume
C.C. timetime
D.D. weightweight

7. How many stars are in the Universe?
300 Sextillion Stars

8. What is Scientific Notation?What is Scientific Notation?
Scientific notation = expressing really bigScientific notation = expressing really big
numbers or really small numbers…numbers or really small numbers…
IN A CONCISE WAY!IN A CONCISE WAY!

9. Scientific notation consists ofScientific notation consists of
two parts:two parts:
1. A number between 1 and 101. A number between 1 and 10
2.2.A power ofA power of 1010
N x 10N x 10xx

10. To change standard form toTo change standard form to
scientific notation…scientific notation…
1.1. Place the decimal point so that there is one non-zeroPlace the decimal point so that there is one non-zero
digit to the left of the decimal point.digit to the left of the decimal point.
2.2. Count the number of decimal places the decimalCount the number of decimal places the decimal
point has “moved” from the original number. Thispoint has “moved” from the original number. This
will be the exponent of the 10.will be the exponent of the 10.
33. If original number is less than 1 = negative exponent. If original number is less than 1 = negative exponent
If the original number is > 1 = positive exponentIf the original number is > 1 = positive exponent

11. ExamplesExamples
Given: 289,800,000Given: 289,800,000
2.8989 x 109
Given: 0.000567Given: 0.000567
5.67 x 10-4

12. To change scientific notationTo change scientific notation
to standard form…to standard form…
Simply move the decimal point to the rightSimply move the decimal point to the right
for positive exponent 10.for positive exponent 10.
Move the decimal point to the left forMove the decimal point to the left for
negative exponent 10.negative exponent 10.
(Use zeros to fill in places.)(Use zeros to fill in places.)

13. ExampleExample
Given: 5.093 x 10Given: 5.093 x 1066
5,093,0005,093,000
Given: 1.976 x 10Given: 1.976 x 10-4-4
0.00019760.0001976

14. Warm-Up:
 Express these numbers in ScientificExpress these numbers in Scientific
Notation:Notation:
1)1) 405789405789
2)2) 0.0038720.003872
3)3) 30000000003000000000
4)4) 22

15. Metric PrefixesMetric Prefixes

16. Metric PrefixesMetric Prefixes
Kilo-Kilo- means 1000 of that unitmeans 1000 of that unit
◦ 1 kilometer (km) = 1000 meters (m)1 kilometer (km) = 1000 meters (m)
Centi-Centi- means 1/100 of that unitmeans 1/100 of that unit
◦ 1 meter (m) = 100 centimeters (cm)1 meter (m) = 100 centimeters (cm)
Milli-Milli- means 1/1000 of that unitmeans 1/1000 of that unit
◦ 1 Liter (L) = 1000 milliliters (mL)1 Liter (L) = 1000 milliliters (mL)

17. Metric Conversions
“King Henry Died by Drinking Chocolate
Milk”
K H D b D C M
1) 2400 g = _____ kg
2) 0.24 L = _____ mL
3) 0.3 hm = _____ m
4) 0.10 ms = _____ sec

18. Learning Check
1. 1000 m = 11. 1000 m = 1 ______ a) mm b) km c) dma) mm b) km c) dm
2. 0.001 g = 12. 0.001 g = 1 ______ a) mg b) kg c) dga) mg b) kg c) dg
3. 0.1 L = 13. 0.1 L = 1 ______ a) mL b) cL c) dLa) mL b) cL c) dL
4. 0.01 m = 1 ___4. 0.01 m = 1 ___ a) mm b) cm c) dma) mm b) cm c) dm

19. Reading a Meter stickReading a Meter stick
First digit (known)First digit (known) ==
Second digit (known)Second digit (known) ==
Third digit (estimated) =Third digit (estimated) =
Length reportedLength reported ==

20. Known + Estimated DigitsKnown + Estimated Digits
• Known digitsKnown digits are 100% certain!are 100% certain!
• The third digit is estimated (uncertain)The third digit is estimated (uncertain)
• In the reported length, all three digits (ex. =In the reported length, all three digits (ex. =
2.75 cm) are significant2.75 cm) are significant includingincluding thethe
estimated one.estimated one.
CERTAIN + ESTIMATED = Significant Digits!CERTAIN + ESTIMATED = Significant Digits!

21. Learning CheckLearning Check
What is the length of the line?What is the length of the line?
How does your answer compare with yourHow does your answer compare with your
neighbor’s answer? Why or why not?neighbor’s answer? Why or why not?

22. Measuring Volume
Make sure
you’re at eye
level.
Take
measurement at
the bottom of
the concave
meniscus.

23. Always estimateAlways estimate ONEONE place past the smallest mark!place past the smallest mark!

24. Three targetsThree targets
with threewith three
arrows each toarrows each to
shoot.shoot.
Can you hit the bull's-eye?Can you hit the bull's-eye?
Can you define accuracy and precision?Can you define accuracy and precision?

25. Accuracy Vs. Precision
Accuracy:
How close a measured value is to the accepted/true
value.
Precision:
How close a series of measurements are to one another.
◦ Note: they may NOT be accurate

26. Conversion Factors
Expresses an equal quantity of one unit to
another.
1 in. = 2.54 cm or 1 inch per 2.54 cm.
: 1 in. and 2.54 cm
2.54 cm 1 in.
EXAMPLE: How many students are in this
class?

27. Learning Check
Write conversion factors that relate each ofWrite conversion factors that relate each of
the following pairs of units:the following pairs of units:
1. Liters and mL1. Liters and mL
2. Hours and minutes2. Hours and minutes
3. Meters and kilometers3. Meters and kilometers

28. How many minutes are in 2.5 hours?
Dimensional Analysis

29. Sample Problem
If you have lived for 52,200 hours, howIf you have lived for 52,200 hours, how
long were you alive in years? (Rememberlong were you alive in years? (Remember
SIG FIGS!)SIG FIGS!)

30. Learning CheckLearning Check
An adult human has 4.65 L of blood. How manyAn adult human has 4.65 L of blood. How many
gallons of blood is that?gallons of blood is that?
Unit plan L qt gallon
Equalities:
1.06 qt = 1.0 L
1 gallon = 4 quarts
Setup:

31. You Try This One!You Try This One!
If Jacob stands on Spencer’sIf Jacob stands on Spencer’s
shoulders, they are two and ashoulders, they are two and a
half yards high. How manyhalf yards high. How many
inches is that?inches is that?

32. Learning Check
How many seconds are in 1.4 days?
Unit plan: days hr min seconds

33. Wait a minute!
What isWhat is wrongwrong with the following setup?with the following setup?
1.4 day x1.4 day x 1 day1 day xx 60 min60 min xx 60 sec60 sec
24 hr 1 hr 1 min24 hr 1 hr 1 min

34. Dealing with Two Units
If your pace on a treadmill is 65 meters perIf your pace on a treadmill is 65 meters per
minute, what is your speed in miles perminute, what is your speed in miles per
hour?hour?

35. Sample Problem
The United States uses 18,000,000 gallons of gasoline
per day. How many liters are used each minute?

36. Sample Problem
Potatoes sell 5 dollars for a 10 pound bag. How much
does one gram of potatoes cost?

37. What about Square and Cubic units?
 Cubed Unit = CUBED NUMBER!Cubed Unit = CUBED NUMBER!
 Best way: Square or cube the ENTIREBest way: Square or cube the ENTIRE
conversion factor.conversion factor.
 Example: Convert 4.3 cmExample: Convert 4.3 cm33
to mmto mm33

38. Learning CheckLearning Check
A Nalgene waterA Nalgene water
bottle holds 1000bottle holds 1000
cmcm33
of dihydrogenof dihydrogen
monoxide. Howmonoxide. How
many cubic metersmany cubic meters
is that?is that?

39. SolutionSolution
1000 cm1000 cm33

40. Significant Figures
• The numbers reported in a measurement
are limited by the measuring tool.
• Significant figures
• All KNOWN Digits
• One ESTIMATED Digit

41. Counting Significant Figures
RULE 1. All non-zero digits in a measured number are
significant.
Sig Figs
38.15 cm ___
5.6 ft ___
65.6 lb ___
122.55 m ___

42. Leading Zeros
RULE 2. Leading zeros in decimal numbers are
NOT significant.
Sig Figs
0.008 mm ____
0.0156 oz ____
0.0042 lb ____
0.000262 mL ____

43. Sandwiched Zeros
RULE 3. Zeros between nonzero numbers are
significant.
Sig Figs
50.8 mm _____
2001 min _____
0.702 lb _____
0.00405 m _____

44. Trailing Zeros
RULE 4. Trailing zeros in numbers without
decimals are NOT significant. Any final zero used
after a decimal point is significant.
Sig Figs
25,000 in. ____
200.30 yr ____
4.320 gal ____
25,005,000 g ____

45. Learning Check
In which set(s) do both numbers contain
the same number of significant figures?
1) 22.0 and 22.00
2) 400.0 and 40
3) 0.000015 and 150,000

46. Learning CheckLearning Check
State the number of significant figures in each of theState the number of significant figures in each of the
following:following:
A. 0.030 mA. 0.030 m ______________
B. 4.050 LB. 4.050 L ______________
C. 0.0008 gC. 0.0008 g ______________
D. 3.00 mD. 3.00 m ______________
E. 2,080,000 beesE. 2,080,000 bees ______________

47. Rounding Significant Figures
1) Round 2.0345 g to 3 sig figs.
2) Round 0.000455 to 2 sig figs.

48. Learning Check
A. Which answers contain 3 significant figures?
1) 0.4760 2) 0.00476 3) 4760
B. All the zeros are significant in
1) 0.00307 2) 25.300 3) 2.050 x 103
C. 534,675 rounded to 3 significant figures is
1) 535 2) 535,000 3) 5.35 x 105

49. Significant Numbers in Calculations
• A calculated answer cannot be more
precise than the measuring tool.
• A calculated answer must match the
least precise measurement.

50. Adding and Subtracting
The answer = same number of decimal places as
the measurement with the fewest decimal places.
25.2 one decimal place
+ 1.34 two decimal places
26.54
answer 26.5 (rounded to one decimal place)

51. Learning Check
In each calculation, round the answer to theIn each calculation, round the answer to the
correct number of sig figs.correct number of sig figs.
A. 235.05 + 19.6 + 2.1 =A. 235.05 + 19.6 + 2.1 =
1) 256.751) 256.75 2) 256.82) 256.8 3) 2573) 257
B. 58.925 - 18.2B. 58.925 - 18.2 ==
1) 40.7251) 40.725 2) 40.732) 40.73 3) 40.73) 40.7

52. Multiplying and Dividing
Answer = the same number of significant
figures as the measurement with the
fewest significant figures.
What’s wrong with this answer?
28.2 x 3.5 = 98.7

53. Learning CheckLearning Check
A. 2.19 x 4.2 =A. 2.19 x 4.2 =
1) 91) 9 2) 9.22) 9.2 3) 9.1983) 9.198
B. 4.311 ÷ 0.07 =B. 4.311 ÷ 0.07 =
1)1)61.5861.58 2) 622) 62 3) 603) 60
C.C. (2.54 x 0.0028) =(2.54 x 0.0028) =
(0.0105 x 0.060)(0.0105 x 0.060)
1) 11.31) 11.3 2) 112) 11 3) 0.0413) 0.041

54. DENSITYDENSITY - an important and useful- an important and useful
physical propertyphysical property
Density = mass (g)
volume (cm3)
Density = mass (g)
volume (cm3)
Mercury
13.6 g/cm13.6 g/cm33
21.5 g/cm21.5 g/cm33
Aluminum
2.7 g/cm2.7 g/cm33
Platinum

55. ProblemProblem A piece of copper has a mass ofA piece of copper has a mass of
57.54 g. It is 9.36 cm long, 7.23 cm wide,57.54 g. It is 9.36 cm long, 7.23 cm wide,
and 0.95 mm thick. Calculate densityand 0.95 mm thick. Calculate density
(g/cm(g/cm33
).).
Density = mass (g)
volume (cm3)
Density = mass (g)
volume (cm3)

56. StrategyStrategy
1. Get dimensions in common units.1. Get dimensions in common units.
2.2. Calculate volume in cubic centimeters.Calculate volume in cubic centimeters.
3. Calculate the density.3. Calculate the density.

57. SOLUTIONSOLUTION
1. Get dimensions in common units.1. Get dimensions in common units.
2.2. Calculate volume in cubic centimeters.Calculate volume in cubic centimeters.
3. Calculate the density.3. Calculate the density.
0.95 mm •
1cm
10 mm
= 0.095 cm
57.54 g
6.4 cm3
= 9.0 g/ cm3
(9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm(9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm33
Note only 2 significant figures in the answer!Note only 2 significant figures in the answer!

58. PROBLEM: Mercury (Hg) has a density of 13.6PROBLEM: Mercury (Hg) has a density of 13.6
g/cmg/cm33
. What is the mass of 95 mL of Hg in grams?. What is the mass of 95 mL of Hg in grams?
In pounds?In pounds?
PROBLEM: Mercury (Hg) has a density of 13.6PROBLEM: Mercury (Hg) has a density of 13.6
g/cmg/cm33
. What is the mass of 95 mL of Hg in grams?. What is the mass of 95 mL of Hg in grams?
In pounds?In pounds?

59. PROBLEM: Mercury (Hg) has a density of 13.6 g/cmPROBLEM: Mercury (Hg) has a density of 13.6 g/cm33
..
What is the mass of 95 mL of Hg?What is the mass of 95 mL of Hg?
PROBLEM: Mercury (Hg) has a density of 13.6 g/cmPROBLEM: Mercury (Hg) has a density of 13.6 g/cm33
..
What is the mass of 95 mL of Hg?What is the mass of 95 mL of Hg?
StrategyStrategy
1.1. Use density to calc. mass (g) fromUse density to calc. mass (g) from volume.volume.
2.2. Convert mass (g) to mass (lb)Convert mass (g) to mass (lb)
Need to know conversion factorNeed to know conversion factor
= 454 g / 1 lb= 454 g / 1 lb
First, note thatFirst, note that 1 cm1 cm33
= 1 mL= 1 mL

60. PROBLEM: Mercury (Hg) has a density of 13.6 g/cmPROBLEM: Mercury (Hg) has a density of 13.6 g/cm33
..
What is the mass of 95 mL of Hg?What is the mass of 95 mL of Hg?
PROBLEM: Mercury (Hg) has a density of 13.6 g/cmPROBLEM: Mercury (Hg) has a density of 13.6 g/cm33
..
What is the mass of 95 mL of Hg?What is the mass of 95 mL of Hg?
1.1. Convert volume to massConvert volume to mass
95 cm3
•
13.6 g
cm3
= 1.3 x 103
g
1.3 x 103
g •
1 lb
454 g
= 2.8 lb
2.2. Convert mass (g) to mass (lb)Convert mass (g) to mass (lb)

61. Learning CheckLearning Check
Osmium is a very dense metal. What is itsOsmium is a very dense metal. What is its
density in g/cmdensity in g/cm33
if 50.00 g of the metal occupiesif 50.00 g of the metal occupies
a volume of 2.22cma volume of 2.22cm33
??
1) 2.25 g/cm1) 2.25 g/cm33
2)2) 22.5 g/cm22.5 g/cm33
3)3) 111 g/cm111 g/cm33

62. Solution
2) Placing the mass and volume of the osmium metal2) Placing the mass and volume of the osmium metal
into the density setup, we obtaininto the density setup, we obtain
D =D = massmass == 50.00 g50.00 g ==
volumevolume2.22 cm2.22 cm33
= 22.522522 g/cm= 22.522522 g/cm33
= 22.5 g/cm= 22.5 g/cm33

63. Volume DisplacementVolume Displacement
A solid displaces a matching volume of waterA solid displaces a matching volume of water
when the solid is placed in water.when the solid is placed in water.
33 mL33 mL
25 mL25 mL

64. Learning CheckLearning Check
What is the density (g/cmWhat is the density (g/cm33
) of 48 g of a metal if the) of 48 g of a metal if the
metal raises the level of water in a graduatedmetal raises the level of water in a graduated
cylinder from 25 mL to 33 mL?cylinder from 25 mL to 33 mL?
1) 0.2 g/ cm1) 0.2 g/ cm33
2) 6 g/m2) 6 g/m33
3) 252 g/cm3) 252 g/cm33
33 mL33 mL
25 mL25 mL

65. Learning CheckLearning Check
Which diagram represents the liquid layers in theWhich diagram represents the liquid layers in the
cylinder?cylinder?
(K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91(K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91
g/mL,) (W) water (1.0 g/mL)g/mL,) (W) water (1.0 g/mL)
1)1) 2)2) 3)3)
K
K
W
W
W
V
V
V
K

66. Learning CheckLearning Check
The density of octane, a component of gasoline, isThe density of octane, a component of gasoline, is
0.702 g/mL. What is the mass, in kg, of 875 mL of0.702 g/mL. What is the mass, in kg, of 875 mL of
octane?octane?
1) 0.614 kg1) 0.614 kg
2) 614 kg2) 614 kg
3) 1.25 kg3) 1.25 kg

67. Learning CheckLearning Check
If blood has a density of 1.05 g/mL, howIf blood has a density of 1.05 g/mL, how
many liters of blood are donated if 575 g ofmany liters of blood are donated if 575 g of
blood are given?blood are given?
1)1) 0.548 L0.548 L
2)2) 1.25 L1.25 L
3)3) 1.83 L1.83 L

68. Learning CheckLearning Check
A group of students collected 125 empty aluminumA group of students collected 125 empty aluminum
cans to take to the recycling center. If 21 cans makecans to take to the recycling center. If 21 cans make
1.0 pound of aluminum, how many liters of1.0 pound of aluminum, how many liters of
aluminum (D=2.70 g/cmaluminum (D=2.70 g/cm33
) are obtained from the) are obtained from the
cans?cans?
1) 1.0 L1) 1.0 L 2) 2.0 L2) 2.0 L 3) 4.0 L3) 4.0 L