Transcript Unit 8A Math and Measurement

Math Concepts
How can a chemist achieve
exactness in measurements?
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Significant
Digits/figures.
Sig figs = the
reliable numbers in
a measurement
and at least one
estimated digit.
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Make readings for the following
measurements using significant figures.
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1.
Rules for significant figures
All non-zero numbers
or digits are significant.
Ex: 23 g
2. All zero in-between 2
non-zero numbers are
significant. Ex: 2.002g
3. When working with a
small decimal number,
work your way over to
the right until you get to
your 1st non-zero
number - anything from
there over is significant.
Ex: 0.00250g
4. Final zeros 25.00g
are significant.
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5. When working with
large numbers (no
decimals), look for your 1st
non-zero number –
anything from there to the
beginning of the number
are significant. Ex:
240100g
6. A line/bar over or
under a zero designates it
as significant.
7. Exact numbers =
numbers that you are use
to working with are
unlimited in terms of
significant figs. Ex: there
are 12 men on the football
field. = unlimited.
Significant Figures
An easy way to count the number of
significant figures in any number is:
DOT LEFT – NOT RIGHT
*If there is a visible decimal, look all the way
to the left of the value and move to the
right. Begin counting digits after your first
non-zero digit. Any numbers that follow a
non-zero digit are significant.
EX: 2.500 = 4 sig figs
500.00 = 5 sig figs
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*If there is no visible decimal, look all the
way to the right of the value and move to
the left. Begin counting digits after your
first non-zero digit. Any numbers that
precede a non-zero digit are significant.
EX: 2500 = 2 sig figs
50000 = 1 sig figs
5001
= 4 sig figs
Examples
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How many sig
figs are in the
following:
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20 kg
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2 sig figs
90.4˚C
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2 sig figs
0.010 s
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3 sig figs
0.004 cm
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1 sig fig
6 sig figs
5310 g
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unlimited
2.15000 cm
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4 sig figs
20 cars
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3 sig figs
100.0˚C
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2 sig figs
0.00900 l
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2 sig figs
11 m
0.089 kg
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1 sig fig
0.0051 g
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3 sig figs
12050 m
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4 sig figs
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If an exponential number, look at
coefficient only.
If decimal at end all numbers are
significant.
A line over a zero indicates that zero as the
last significant digit.
Use decimal or line, not both.
No lines over nonzero digits.
Calculations using sig figs
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Adding or subtracting:
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Look at the decimal
places. Choose the given
information that has the
least number of decimal
places. Make sure to put
your answers in the least
number of decimals.
Your calculator does not
do this! Your final
measurement can not be
more specific than your
least specific
measurement!
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Multiplying or dividing:
Identify sig figs for each
number in your
information. Your
answer needs to be
altered to the least
number of sig figs used
when solving the
problem. (for the same
reason)
Addition
Subtraction
Multiplication
Division
Practice:
1. Give the correct number of significant figures
for:
4500
4500.
0.0032
0.04050
2. 4503 + 34.90 + 550 = ?
3. 1.367 - 1.34 = ?
4. (1.3 x 103)(5.724 x 104) = ?
5. (6305)/(0.010) = ?
Scientific Notation
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Why is it that we use scientific notation in
science?
because many of the numbers, amount,
etc. that we use are either really big or
very small.
Examples: Distance from the Earth to the
Sun, size of an atom, the mass of an
electron, proton, or even neutron…..
Scientific Notation
If the number is large –
you will have a positive
exponent
 If the number is very
small – you will have a
negative exponent.
 Exponent decides which
direction and how many
spots you will move the
decimal
EX: 10000 = 1 x 104
0.00044 = 4.4 x 10-4
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Must honor sig figs in
original value
 Root number or
coefficient is the only
number that is
significant (exponent
does not count)
EX: 2.4327 x 104
5 sig figs
7.8 x 10-3
2 sig figs
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Examples
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What is the correct scientific notation for:
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25000
.00000801
12.87
What is the correct standard notation for:
1.98 x 103
2.609 x 10 -2
3.81 x 10-5
0.070 x 105
0.005 x 10-3
Calculations with scientific notation
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Multiplication:
multiply the
coefficients(roots)
and add your
exponents
Division: divide the
coefficients(roots)
and subtract your
exponents
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Add or subtract:
Change your
exponents to equal
(largest one), then add
and put back into
correct scientific
notation. OR put your
numbers in standard
notation +/- and then
place back into
scientific notation
Practice:
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(2.68 x
(2.95 x
(8.41 x
(9.21 x
(4.52 x
(1.74 x
(2.71 x
(4.56 x
x 103)
(3.05 x
10-5) x (4.40 x 10-8)
107) ÷ (6.28 x 1015)
106) x (5.02 x 1012)
10-4) ÷ (7.60 x 105)
10-5) + (1.24 x 10-2) + (3.70 x 10-4) +
10-3)
106) - (5.00 x 104)
106) + (2.98 x 105) + (3.65 x 104) + (7.21
106) x (4.55 x 10-10)
How can you decide if your
experiments are accurate/precise?
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Percent error = calculations that will give
you a percent deviation from the true
value.
Formula: l True – experimental l x 100
True
Example
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A student measured the density of an object to
be 2.889 g/ml, the true density of the object is
2.699g/ml. What is the percent error of the
experiment? Is the student accurate?
ANSWER: 7.040% error, anything below
10% is acceptable as accurate. The closer
to 0% the better!
Metric Conversions
Conversion Practice: *honor sig figs
550 cm  m
1500 mL  liters
3500 mg  g
0.750 liters  mL
1.50 m  cm
1.250 liters  mL
40 mL  liters
1500 mL  cm3
270 cm3  mL
2560 cm3  liters
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Dimensional Analysis
Used to convert between units of measurement
using equivalent values.
EX: Convert 800.0 grams into pounds
Step 1: Place given value over 1.
Step 2: Select appropriate conversion factor (454
grams = 1 lb) and place in parenthesis so that the
unit of the given will cancel with the same unit in
the conversion factor.
Step 3: Continue conversion factors until the only unit
remaining is the one that you want.
Step 4: Divide the product of the numerator by the
product of the denominator.
Step 5: Express answer in correct sig figs and unit.
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800.0 g ( 1 lb ) =
1
(454 g )
1.762 lb
Common Conversion Factors:
2.54 cm = 1 inch
16 oz = 1 lb
454 grams = 1 pound
12 inch = 1 ft
5280 feet = 1 mile
1 L = 1.06 quarts
4 quarts = 1 gallon
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Convert:
25.0 inches  cm
2.45 pounds  grams
2500 grams  pounds
500.0 cm  inches
750 cm  feet
27000 cm  miles
0.002570 years  minutes
*45 miles/hour  km/minute
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