Transcript Measurement and Dimensional Analysis

Measurement
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Accuracy vs Precision
Percent Error
Significant Figures
Scientific Notation
Temperature Conversions
Dimensional Analysis
Conversion Factors
SI Conversions
Number vs. Quantity
• Quantity = number + unit
UNITS MATTER!!
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
A. Accuracy vs. Precision
B. Percent Error
• Indicates accuracy of a measurement
% error 
experimental  accepted
accepted
your value
given value
 100
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.
% error 
1.40 g/mL  1.36 g/mL
1.36 g/mL
% error = 2.94 %
 100
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
2.31 cm
C. Significant Figures
• Counting Sig Figs
– Digits from 1-9 are always significant
739
– Zeros between two other sig figs are always
significant 5085
– One or more additional zeros to the right of both
the decimal place and another sig digit are
significant
2.60
– Count all numbers EXCEPT:
• Leading zeros -- 0.0025
• Trailing zeros without
a decimal point -- 2,500
C. Significant Figures
Counting Sig Fig Examples
1. 23.50
4 sig figs
2. 402
3 sig figs
3. 5,280
3 sig figs
4. 0.080
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
(13.91g/cm3)(23.3cm3) = 324.103g
4 SF
3 SF
3 SF
324 g
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  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
C. Significant Figures
Practice Problems
5. (15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= 2.390625 g/mL  2.4 g/mL
2 SF
6. 18.9 g
- 0.84 g
18.06 g  18.1 g
D. Scientific Notation
• A way to express any number as a number
between 1 and 10 (coefficient) multiplied by 10
raised to a power (exponent)
• Number of carbon atoms in the Hope diamond
• 460,000,000,000,000,000,000,000 atoms
• 4.6 x 1023 atoms
coefficient
exponent
D. Scientific Notation
65,000 kg  6.5 × 104 kg
• 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 – all of them!
D. Scientific Notation
Practice Problems
7.
8.
9.
2,400,000 g
2.4 
0.00256 kg
2.56 
7.0  10-5 km
10. 6.2  104 mm
6
10
g
-3
10
kg
0.000070 km
62,000 mm
D. Scientific Notation
• Calculating with Sci. Notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
Type on your calculator:
5.44
EXP
EE
7
÷
8.1
EXP
EE
4
EXE
ENTER
= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
D. Scientific Notation
Practice Problems
4  1010 cm2
11. (4 x 102 cm) x (1 x 108cm)
12. (2.1 x 10-4kg) x (3.3 x 102 kg)
6.9  10-2 kg2
13. (6.25 x 102) ÷ (5.5 x 108)
1.1 x 10-6
14. (8.15 x 104) ÷ (4.39 x 101)
1.86 x 103
15. (6.02 x
5.01 x 1022
1023)
÷ (1.201 x
101)
E. Temperature
• Temperature
– measure of the average KE of the
particles in a sample of matter
Kelvin  oC  273.15
9o
Fahrenheit 
C  32
5
5o
Celsius 
F  32
9
E. Temperature
•
Convert these temperatures:
298.15
______________K
1)
25oC
2)
298
-15oF = ______________
K
3)
41.85
oC
315K = ______________
4)
298
288K = ______________ oF
=
F. Dimensional Analysis
• Dimensional Analysis is also called Unit
Analysis and is a great way to solve
problems in chemistry (or any time).
F. Dimensional Analysis
• Dimensional Analysis
– A tool often used in science for converting units
within a measurement system
• Conversion Factor
– A numerical factor by which a quantity expressed in
one system of units may be converted to another
system
F. Dimensional Analysis
Problem-Solving Steps
1. Analyze
2. Plan
3. Compute
4. Evaluate
F. Dimensional Analysis
• The “Factor-Label” Method
– Units, or “labels” are canceled, or “factored” out
g
3
cm 

3
cm
g
F. Dimensional Analysis
• Steps to solving problems:
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.
G. Conversion Factors
Fractions in which the numerator and
denominator are EQUAL quantities expressed
in different units
Example:
1 in. = 2.54 cm
Factors: 1 in.
and
2.54 cm
2.54 cm
1 in.
How many minutes are in 2.5 hours?
Conversion factor
2.5 hr x
1
cancel
60 min
1 hr
= 150 min
G. Conversion Factors
Write conversion factors that relate
each of the following pairs of units:
1. Liters and mL
1 L = 1000 mL
1L
1000 mL
2. Hours and minutes
3. Meters and kilometers
1 hr
60 min
1000 m
1 km
H. SI Prefix Conversions
1. Memorize the following chart. (next slide)
2. Find the conversion factor(s).
3. Insert the conversion factor(s) to get to the correct
units.
4. When converting to or from a base unit, there will
only be one step. To convert to or from any other
units, there will be two steps.
H. SI Prefix Conversions
move right
move left
Prefix
teragigamegakilohectodekaBASE UNIT
decicentimillimicronano-
Symbol
T
G
M
k
h
da
--d
c
m

n
Factor
1012
109
106
103
102
101
100
10-1
10-2
10-3
10-6
10-9
H. SI Prefix Conversions
a. cm to m
b. m to µm
c. ns to s
d. kg to g
1m
100 cm
1m
106 µm
1s
109 ns
1 kg
1000 g
H. SI Prefix Conversions
4) 805 Tb =
14
8.05
x
10
______________ b
bytes
Terabytes
1012 b
805 Tb
1
= 805 x 1012 bytes
1 Tb
= 8.05 x 1014 bytes

H. SI Prefix Conversions
5) 400. g = ______________ kg
6) 57 Mm =
______________ nm
Dimensional Analysis Practice
1. You have $7.25 in your pocket in
quarters. How many quarters do you
have?
2. How many seconds are in 1.4
days?
Plan: days
hr
min
seconds
3. How many milliliters are in 1.00 quart of milk?
4. You have 1.5 pounds of gold. Find its volume
in cm3 if the density of gold is 19.3 g/cm3.
5. Your European hairdresser wants to cut your
hair 8.0 cm shorter. How many inches will he be
cutting off?
6. Milton football needs 5.5 yards for a 1st down.
How many cm is this?
7. A piece of wire is 1.3 m long. How many 1.5cm pieces can be cut from this wire?
8. How many liters of water would fill a container
that measures 75.0 in3?