i ii iii i. using measurements measurement. a. accuracy vs. precision accuracy - how close a...
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I
II
III
I. Using Measurements
MEASUREMENT
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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 = CORRECT
PRECISE = 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 = 2.9 %
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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
Count all numbers EXCEPT:
Leading zeros -- 0.0025
Trailing zeros without a decimal point -- 2,500
Captive zeros– 20004
Always count
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4. 0.080
3. 5,280
2. 402
1. 23.50
C. 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 Figures
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 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.
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 Figures
Calculating with Sig Figs (con’t)
Exact Numbers do not limit the # of sig figs in the answer.Counting numbers: 12 studentsExact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm
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C. Significant Figures
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 exponentSmall # (<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
2.4 106 g
2.56 10-3 kg
0.00007 km
62,000 mm
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D. Scientific 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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I
II
III
II. Units of Measurement
MEASUREMENT
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A. Number vs. Quantity
Quantity - number + unit
UNITS MATTER!!
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B. SI Units
Quantity Base Unit Abbrev.
Length
Mass
Volume
Temp
meter
gram
liter
Kelvin
m
g
l
K
Amount mole mol
Symbol
l
m
v
T
n
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B. SI Units
Prefix Symbol FactorGiga G 109
Mega M 106
Kilo k 103
BASE UNIT -- 100
Deci d 10-1
Centi c 10-2
Milli m 10-3
Micro 10-6
Nano n 10-9
Pico p 10-12
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C. 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 g
V
MD
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C. 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 = 25 g
0.87 g/mL
V = 29 mLV
MD
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C. DensityM
ass
(g)
Volume (cm3)
Δx
Δyslope D
V
M
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I
II
III
III. Unit Conversions
MEASUREMENT
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A. SI Prefix Conversions
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
NUMBERUNIT
NUMBER
UNIT
532 m = _______ km0.532
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A. SI Units Prefixes
Prefix Symbol FactorGiga G 109
Mega M 106
Kilo k 103
BASE UNIT -- 100
Deci d 10-1
Centi c 10-2
Milli m 10-3
Micro 10-6
Nano n 10-9
Pico p 10-12
mo
ve le
ft
mo
ve r
igh
t
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A. SI Prefix Conversions
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
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 each bottom number.
4. Check units & answer.
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B. Converting SI Units with Dimensional Analysis
Convert 10 liters to centiliters. Identify starting and ending points Starting point 10 liters, ending point centiliters Draw a T chart, you can add boxes as you go Line up conversion factors Then cancel the unit top and bottom Multiply across, divide top by the bottom.
10 liters
1 liter
100 clEnd Point
= 1000 cl or 1 X 103 cl
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How many milligrams are in 50 kilograms? Identify starting and ending points Start at 50 kg; end at mg Draw a T chart, you can add boxes as you go Line up conversion factors Then cancel the unit top and bottom Multiply across, divide top by the bottom
50 kg
1 kg
1000 g
1 g
1000 mg
End Point
= 50,000,000 mg
or 5 X 107 mg
B. Converting SI Units with Dimensional Analysis
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I
II
III
End Unit 1
STOP