Unit 2. Measurement
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Unit 2. Measurement
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Do Now In your own words, what do you think is the
difference between:
Accuracy and Precision?
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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
ACCURATE = CORRECTPRECISE = CONSISTENT
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ACCURATE = CORRECTPRECISE = CONSISTENT
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B. Percent Error Indicates accuracy of a measurement
100literature
literaturealexperimenterror %
your value
accepted value
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B. 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.
100g/mL 1.36
g/mL 1.36g/mL 1.40error %
% error = 2.90 %
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C. Significant Figures Indicate precision of a measurement. Recording Sig Figs
Sig figs in a measurement include the known digits plus a final estimated digit
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C. Significant Figures 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 Figures Counting Sig Figs (Table 2-5, p.47)
Count all numbers EXCEPT:
Leading zeros -- 0.0025 (not significant)
Trailing zeros without a decimal point -- 2,500 (not Significant)
Zeros between numbers are significant
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4. 0.080
3. 5,280
2. 402
1. 23.50
C. Significant FiguresCounting Sig Fig Examples
1. 23.50
2. 402
3. 5,280
4. 0.080
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4. 0.080
3. 5,280
2. 402
1. 23.50
C. Significant FiguresCounting 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 Figures Calculating with Sig Figs
Multiply/Divide –
The # with the fewest sig figs determines the # of sig figs in the answer.
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Multiplication and Division Rules Do the sum Round the answer to the least
significant figure in the problem
13.91g/cm3)(23.3cm3) = 324.103g 4SF 3SF 3SF
324g
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C. 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.
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Addition and Subtraction Rules Stack the numbers so that the decimal
point is aligned Do the sum Figure out which number has least
decimal place (least precise/decimal area least far out)
Draw a line after the last number with the least decimal place
Round the digit by looking at the number that follows
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Example
3.75 mL + 4.1 mL 7.85 mL 7.9 mL
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C. 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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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 Notation
Converting into Sci. 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.
65,000 kg 6.5 × 104 kg
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D. Scientific Notation
7. 2,400,000 g
8. 0.00256 kg
9. 7 10-5 km
10. 6.2 104 mm
Practice Problems
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D. Scientific Notation
7. 2,400,000 g
8. 0.00256 kg
9. 7 10-5 km
10. 6.2 104 mm
Practice Problems
2.4 106 g2.56 10-3 kg
0.00007 km62,000 mm
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D. Scientific Notation Calculating with Sci. Notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
5.44EXPEE
÷EXPEE ENTER
EXE7 8.1 4
= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
Type on your calculator:
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E. Proportions Direct Proportion
Inverse Proportion
xy
xy 1
y
x
y
x
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Units of Measurement
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A. Number vs. Quantity Quantity - number + unit
UNITS MATTER!!
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B. SI UnitsQuantity Base Unit Abbrev.
Length
Mass
TimeTemp
meter
kilogram
secondkelvin
m
kg
sK
Amount mole mol
Symbol
l
m
tTn
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B. SI Unitsmega- 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 Units Combination of base units.
Volume (m3 or cm3) length length length
D = MV
1 cm3 = 1 mL1 dm3 = 1 L
Density (kg/m3 or g/mL or g/cm3)
mass per volume
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D. Density
Mas
s (g
)
Volume (cm3)
ΔxΔyslope D
VM
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Problem-Solving Steps
1. Analyze
2. Plan
3. Compute
4. Evaluate
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D. Density An object has a volume of 825 cm3 and a density of
13.6 g/cm3. Find its mass.
GIVEN:V = 825 cm3
D = 13.6 g/cm3
M = ?
WORK:
VMD
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D. Density An object has a volume of 825 cm3 and a density of
13.6 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 gVMD
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D. 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/mLV = ?M = 25 g
WORK:
VMD
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D. 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/mLV = ?M = 25 g
WORK:V = M D
V = 25 g 0.87 g/mLV = 29 mLV
MD
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III. Unit Conversions
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A. SI Prefix Conversions1. 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 Conversionsmega- 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
mov
e le
ftm
ove
right
BASE UNIT --- 100
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A. SI Prefix Conversions1) 20 cm = ______________ m
2) 0.032 L = _____________ mL
3) 45 m = ______________ nm
4) 805 dm = ______________ km
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C. Johannesson
A. SI Prefix Conversions1) 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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33
cmgcm
B. Dimensional Analysis The “Factor-Label” Method
Units, or “labels” are canceled, or “factored” out
g
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B. Dimensional Analysis Steps:
1. Identify starting & ending units.2. Line up conversion factors so units
cancel.3. Multiply all top numbers & divide by
bottom number.4. Check units & answer.
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B. Dimensional Analysis Lining up conversion factors:
ARE THESE THE SAME?1 in = 2.54 cm
2.54 cm 2.54 cm
1 in = 2.54 cm 1 in 1 in
= 1
1 =
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B. Dimensional Analysis
How many milliliters are in 1.00 quart of milk?
1.00 qt 1 L1.057 qt
= 946 mL
qt mL
1000 mL1 L
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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.
lb cm3
1.5 lb 1 kg2.2 lb
= 35 cm31000 g
1 kg1 cm3
19.3 g
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B. Dimensional Analysis 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 L1000 cm3
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B. Dimensional Analysis
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 in2.54 cm
= 3.2 in
cm in
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B. Dimensional Analysis6) Taft football needs 550 cm for a 1st down. How
many yards is this?
550 cm 1 in2.54 cm
= 6.0 yd
cm yd
1 ft12 in
1 yd3 ft
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B. Dimensional Analysis7) 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 cm1 m
= 86 pieces
cm pieces
1 piece1.5 cm