unit 2. measurement. do now in your own words, what do you think is the difference between: ...
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Unit 2. Measurement
Do Now In your own words, what do you think is the
difference between:
Accuracy and 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
ACCURATE = CORRECT
PRECISE = CONSISTENT
ACCURATE = CORRECTPRECISE = CONSISTENT
B. Percent Error
Indicates accuracy of a measurement
100literature
literaturealexperimenterror %
your value
accepted value
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 %
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
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
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
4. 0.080
3. 5,280
2. 402
1. 23.50
C. Significant Figures
Counting Sig Fig Examples1. 23.50
2. 402
3. 5,280
4. 0.080
4. 0.080
3. 5,280
2. 402
1. 23.50
C. Significant Figures
Counting Sig Fig Examples1. 23.50
2. 402
3. 5,280
4. 0.080
4 sig figs
3 sig figs
3 sig figs
2 sig figs
C. Significant Figures Calculating with Sig Figs
Multiply/Divide –
The # with the fewest sig figs determines the # of sig figs in the answer.
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
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.
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
Example
3.75 mL + 4.1 mL 7.85 mL 7.9 mL
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
5. (15.30 g) ÷ (6.4 mL)
Practice Problems
= 2.390625 g/mL
18.1 g
6. 18.9 g
- 0.84 g
18.06 g
4 SF 2 SF
2.4 g/mL
2 SF
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
D. Scientific Notation
7. 2,400,000
g
8. 0.00256
kg
9. 7 10-5
km
10. 6.2 104
mm
Practice Problems
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
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:
E. Proportions Direct Proportion
Inverse Proportion
xy
xy
1
y
x
y
x
Units of Measurement
A. Number vs. Quantity
Quantity - number + unit
UNITS MATTER!!
B. SI UnitsQuantity Base Unit Abbrev.
Length
Mass
Time
Temp
meter
kilogram
second
kelvin
m
kg
s
K
Amount mole mol
Symbol
l
m
t
T
n
B. 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
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
D. Density
Mas
s (g
)
Volume (cm3)
Δx
Δyslope D
V
M
Problem-Solving Steps
1. Analyze
2. Plan
3. Compute
4. Evaluate
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:
V
MD
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 gV
MD
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/mL
V = ?
M = 25 g
WORK:
V
MD
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/mL
V = ?
M = 25 g
WORK:
V = M D
V = 25 g
0.87 g/mLV = 29 mLV
MD
III. Unit Conversions
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?
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
mo
ve le
ft
mo
ve r
igh
t BASE UNIT --- 100
A. SI Prefix Conversions
1) 20 cm = ______________ m
2) 0.032 L = _____________ mL
3) 45 m = ______________ nm
4) 805 dm = ______________ km
C. Johannesson
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
3
3
cm
gcm
B. Dimensional Analysis The “Factor-Label” Method
Units, or “labels” are canceled, or “factored” out
g
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.
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 =
B. Dimensional Analysis
How many milliliters are in 1.00 quart of milk?
1.00 qt 1 L
1.057 qt= 946 mL
qt mL
1000 mL
1 L
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 kg
2.2 lb= 35 cm3
1000 g
1 kg
1 cm3
19.3 g
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 L
1000 cm3
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 in
2.54 cm= 3.2 in
cm in
B. Dimensional Analysis6) Taft 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
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 cm
1 m= 86 pieces
cm pieces
1 piece
1.5 cm