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I. Using MeasurementsI. Using Measurements
MEASUREMENTIN
SCIENCE
MEASUREMENTIN
SCIENCE
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A. Accuracy vs. Precision
A. Accuracy vs. Precision
• Accuracy - how close a measurement is to the accepted value
• Precision - how close a series of measurements are to each other
• Accuracy - how close a measurement is to the accepted value
• Precision - how close a series of measurements are to each other
ACCURATE = CORRECT
PRECISE = REPEATABLE
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B. Percent ErrorB. Percent Error
• Indicates accuracy of a measurement
• Indicates accuracy of a measurement
100literature
literaturealexperimenterror %
your value
accepted value
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B. Percent ErrorB. Percent Error• 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.
• 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.
100g/mL 1.36
g/mL 1.36g/mL 1.40error %
% error = 2.9 %
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C. Significant FiguresC. Significant Figures
• Indicate precision of a measurement.
• Recording Sig Figs• Sig figs in a measurement include the known digits plus a final estimated digit
• Indicate precision of a measurement.
• Recording Sig Figs• Sig figs in a measurement include the known digits plus a final estimated digit
2.35 cm
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C. Significant FiguresC. Significant Figures• Counting Sig Figs
• Count all digits (1-9)
• Zero Rules:• Trapped zeros -- 101
are always significant
• Preceding zeros -- 0.0025
are never significant
• Trailing zeros -- 2500
only with a decimal point
• Counting Sig Figs
• Count all digits (1-9)
• Zero Rules:• Trapped zeros -- 101
are always significant
• Preceding zeros -- 0.0025
are never significant
• Trailing zeros -- 2500
only with a decimal point
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4. 0.080
3. 5,280
2. 402
1. 23.50
C. Significant FiguresC. Significant Figures
Counting Sig Fig Examples
1. 23.50
2. 402
3. 5,280
4. 0.080
4 sig figs
3 sig figs
3 sig figs
2 sig figs
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C. Significant FiguresC. Significant Figures
• Calculating with Sig Figs• Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.
• 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) = 324.103g
324 g
4 SF 3 SF3 SF
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C. Significant FiguresC. Significant Figures• 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.
• 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.
3.75 mL
+ 4.1 mL
7.85 mL
224 g
+ 130 g
354 g 7.9 mL 350 g
3.75 mL
+ 4.1 mL
7.85 mL
224 g
+ 130 g
354 g
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C. Significant FiguresC. 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
• 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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C. Significant FiguresC. Significant Figures
5. (15.30 g) ÷ (6.4 mL)5. (15.30 g) ÷ (6.4 mL)
Practice Problems
= 2.390625 g/mL
18.1 g
6. 18.9 g
- 0.84 g18.06 g
4 SF 2 SF
2.4 g/mL2 SF
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D. Scientific NotationD. Scientific Notation
• Converting into Sci. Notation:
• Move decimal until there’s 1 digit to its left. Places moved = exponent.
• Large # (>1) Þ positive exponent (left) Small # (<1) Þ negative exponent (right)
• Only include sig figs.
• Converting into Sci. Notation:
• Move decimal until there’s 1 digit to its left. Places moved = exponent.
• Large # (>1) Þ positive exponent (left) Small # (<1) Þ negative exponent (right)
• Only include sig figs.
65,000 kg 6.5 × 104 kg
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D. Scientific NotationD. Scientific Notation
7. 2,400,000 g
8. 0.00256 kg
9. 7 10-5 km
10. 6.2 104 mm
7. 2,400,000 g
8. 0.00256 kg
9. 7 10-5 km
10. 6.2 104 mm
Practice Problems
2.4 106 g
2.56 10-3 kg
0.00007 km
62,000 mm
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D. Scientific NotationD. Scientific Notation• Calculating with Sci. Notation• Calculating with Sci. Notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
5.44EXPEXP
EEEE÷÷
EXPEXP
EEEE ENTERENTER
EXEEXE7 8.1 4
= 671.6049383= 670 g/mol
= 6.7 × 102 g/mol
Type on your calculator:
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II. Units of MeasurementII. Units of Measurement
MEASUREMENTMEASUREMENT
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A. Number vs. QuantityA. Number vs. Quantity• Quantity - number + unit• Quantity - number + unit
UNITS MATTER!!
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B. SI UnitsB. SI Units
Quantity Base Unit Unit Abbrev.
Length
Mass
Time
Temp
meter
kilogram
second
kelvin
m
kg
s
K
Amount mole mol
Variable Symbol
l
m
t
T
n
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B. SI UnitsB. SI Units
mega- M 106
deci- d 10-1
centi- c 10-2
milli- m 10-3
Prefix Symbol Factor
micro- 10-6
nano- n 10-9
pico- p 10-12
kilo- k 103
BASE UNIT --- 100
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C. Derived UnitsC. Derived Units
• Combination of base units.• Volume (m3 or cm3) • length x length x length
• Combination of base units.• Volume (m3 or cm3) • length x length x length
1 cm3 = 1 mL1 dm3 = 1 L
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Problem-Solving StepsProblem-Solving Steps
1. Analyze
2. Plan
3. Compute
4. Evaluate
1. Analyze
2. Plan
3. Compute
4. Evaluate
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III. Unit Conversions
(Dimensional Analysis)
III. Unit Conversions
(Dimensional Analysis)
MEASUREMENTMEASUREMENT
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A. SI Prefix Conversions
A. SI Prefix Conversions
1. Find the difference between the exponents of the two prefixes.
2. Move the decimal that many places.
1. Find the difference between the exponents of the two prefixes.
2. Move the decimal that many places.
To the leftor right?
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=
A. SI Prefix Conversions
A. SI Prefix Conversions
NUMBERUNIT
NUMBER
UNIT
532 m = _______ km
0.532
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A. SI Prefix Conversions
A. SI Prefix Conversions
mega- M 106
deci- d 10-1
centi- c 10-2
milli- m 10-3
Prefix Symbol Factor
micro- 10-6
nano- n 10-9
pico- p 10-12
kilo- k 103
move left
move right BASE UNIT --- 100
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A. SI Prefix Conversions
A. SI Prefix Conversions
1) 20 cm = ______________ m
2) 0.032 L = ______________ mL
3) 45 m = ______________ nm
4) 805 dm = ______________ km
1) 20 cm = ______________ m
2) 0.032 L = ______________ mL
3) 45 m = ______________ nm
4) 805 dm = ______________ km
0.2
0.0805
45,000
32
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3
3
cm
gcm
B. Dimensional Analysis
B. Dimensional Analysis
• The “Factor-Label” Method• Units, or “labels” are canceled, or “factored” out
• The “Factor-Label” Method• Units, or “labels” are canceled, or “factored” out
g
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B. Dimensional Analysis
B. Dimensional Analysis
• Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom number.
4. Check units & answer.
• Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom number.
4. Check units & answer.
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B. Dimensional Analysis
B. Dimensional Analysis
• Lining up conversion factors:• Lining up conversion factors:
1 in = 2.54 cm2.54 cm 2.54 cm
1 in = 2.54 cm 1 in 1 in
= 1
1 =
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B. Dimensional Analysis
B. Dimensional Analysis
• How many milliliters are in 1.00 quart of milk?• How many milliliters are in 1.00 quart of milk?
1.00 qt 1 L1.057
qt
= 946 mL
qt mL
1000 mL
1 L
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B. Dimensional Analysis
B. Dimensional Analysis
• You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.
• You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.
lb cm3
1.5 lb1 kg
2.2 lb= 35 cm3
1000 g
1 kg
1 cm3
19.3 g
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B. Dimensional Analysis
B. Dimensional Analysis
• How many liters of water would fill a container that measures 75.0 in3?
• How many liters of water would fill a container that measures 75.0 in3?
75.0 in3
(2.54 cm)3
(1 in)3
= 1.23 L
in3 L
1 L
1000 cm3
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B. Dimensional Analysis
B. Dimensional Analysis
5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?
5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?
8.0 cm
1 in
2.54 cm= 3.2 in
cm in
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B. Dimensional Analysis
B. Dimensional Analysis
6) WF football needs 550 cm for a 1st down. How many yards is this?6) WF football needs 550 cm for a 1st down. How many yards is this?
550 cm 1 in
2.54 cm= 6.0 yd
cm yd
1 ft
12 in
1 yd
3 ft
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B. Dimensional Analysis
B. Dimensional Analysis
7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?
7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?
1.3 m 100 cm
1 m= 86 pieces
cm pieces
1 piece
1.5 cm