Scientific Notation / Significant Figures / Dimensional Analysis

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Unit 1

• Scientific Notation / Significant Figures /
  Dimensional Analysis

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Precision
Accuracy
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Precision -

• How close your results are to each other.
• (A Tight group)

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Accuracy -

• How close your answers are to the accepted
  value.
• (Hitting the Bulls Eye).

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Which (accuracy or precision) is preferred and
why ?

• Precision is preferred.

If you are precise (tight group) all you have to
do is adjust your sights (lab technique if
chemistry). However, if you are all over the
target, those two Bulls Eye shots were probably
luck and not repeatable.)
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Scientific Notation

• A format A10nth for writing numbers where
  A is a number with a single non-zero digit to
  the left of the decimal point, and n is a whole
  number which may be either positive or negative.

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Examples going from standard to scientific
notation.
1) 5000
5 x 103
2) 25,000
2.5 x 104
3) 1,000,000
1. x 106
4) 1,005,000
1.005 x 106
5) 325.005
3.25005 x 102
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Examples going from standard to scientific
notation.
1) 5000
5 x 103
2) 25,000
2.5 x 104
3) 1,000,000
1. x 106
4) 1,005,000
1.005 x 106
5) 325.005
3.25005 x 102
Notice IF YOU MOVED THE DECIMAL TO THE LEFT
THE EXPONENT WILL BE POSITIVE.
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Examples going from standard to scientific
notation.
6) 3.5
3.5 x 100
7) 1.835
1.835 x 100
Notice IF YOU DO NOT MOVE THE DECIMAL
THE EXPONENT WILL BE ZERO.
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Examples going from standard to scientific
notation.
8) 0.5
5 x 10-4
9) 0.05
5 x 10-2
10) 0.008
8 x 10-3
11) 0.5003
5.003 x 10-1
Notice IF YOU MOVED THE DECIMAL TO THE RIGHT
THE EXPONENT WILL BE NEGATIVE.
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Examples going from scientific to standard
notation.
10,000
1) 1 x 104
6,000
2) 6 x 103
150
3) 1.5 x 102
355,000
4) 3.55 x 105
Notice IF THE EXPONENT IS POSITIVE, YOU MOVE
THE DECIMAL TO THE RIGHT.
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Examples going from scientific to standard
notation.
4.11
5) 4.11 x 100
5
6) 5 x 100
4.5678
7) 4.5678 x 100
Notice IF THE EXPONENT IS ZERO, YOU DO NOT
MOVE THE DECIMAL.
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Examples going from scientific to standard
notation.
0.00067
8) 6.7 x 10-4
0.07707
9) 7.707 x 10-2
0.70031
10) 7.0031 x 10-1
0.0100
11) 1.00 x 10-2
Notice IF THE EXPONENT IS NEGATIVE, YOU
MOVE THE DECIMAL TO THE LEFT.
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Significant Figure -

• Those digits in a measured number (or the
  result of calculations with measured numbers)
  that include all certain digits plus a final
  digit with some uncertainty.

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Certain Digit -

• A number whose value is measurable with the
  available equipment.

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Uncertain digit-

• A number whose value is not known to be exact.
  The last digit of a measured number (excluding
  counting). The last digit of a rounded number

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• Example Somebodys old fashioned bathroom
  scale indicates that the person weighs 180 lbs.,
  however the needle lines up a wee bit above the
  actual 180 lb. mark. Does this person weigh
  exactly 180 lbs.?

NO
The last digit is uncertain.
How much does he weigh?
How can better determine this persons weight?
A more precise scale.
How would a digital scale effect this measurement?
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7 Rules for determining significant figures

• 1. All significant numbers must have a decimal
  point

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7 Rules for determining significant figures
(cont.)

• 2. Every non-zero digit in a recorded measuremen
  t is significant.

54.3 mL
Examples
3 sig figs.
0.123 g
3 sig figs.
156. m
3 sig figs.
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7 Rules for determining significant figures
(cont.)

• 3. Zeros appearing between non-zero digits are
  significant.

2304. m
Examples
4 sig figs.
50.05 g
4 sig figs.
12300.09 cm3
7 sig figs.
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7 Rules for determining significant figures
(cont.)

• 4. Zeros at the end of a number and to the
  right of the decimal point are always
  significant

38.50 Km
Examples
4 sig figs.
2.0900 g
5 sig figs.
10,000.00 v
7 sig figs.
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7 Rules for determining significant figures
(cont.)

• 5. Zeros appearing in front of all
  non-zero digits are NOT SIGNIFICANT (they
  are place holders).

0.0067 mL
Examples
2 sig figs.
0.25 mg
2 sig figs.
0.000015 L
2 sig figs.
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7 Rules for determining significant figures
(cont.)

• 6. Zeros at the end of a number and to the left
  of the decimal point are not significant if they
  are just place holders (no decimal or not
  measured).

400. cm
Examples
1 sig figs.
35,700. m
3 sig figs.
3460. mm
3 sig figs.
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7 Rules for determining significant figures
(cont.)

• 7. EXCEPTIONS The following situation have an
  unlimited number of significant figures

A) If counting 25 students in this classroom
means exactly 25 students.
B) Exactly defined quantities (conversion
factors 1in 2.54cm.)
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Calculations with significant figures
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Addition / Subtraction

• When adding or subtracting significant figures,
  do the math. However, when reporting your answer
  the amount of significant figures will be equal
  to no more digits to the right of the decimal as
  the least amount of digits to the right of the
  decimal in the problem. (think place values)

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Example 1
However, using significant figures, the answer
would have only one digit to the right of the
decimal point.

• 234.5
• 14.75
• 6.795

256.045
256.0
Note if the 4 were a five, what would the
answer be?
256.1
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Example 2
However, using significant figures, the answer
would have only one digit to the right of the
decimal point.

• 123.416
• 34.67
• 7.9

165.986
166.0
Notice the effect of rounding.
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Multiplication / Division

• When multiplying or dividing significant
  figures, do the math. However, when reporting
  your answer the amount of significant figures
  will be equal to the least (lowest) number of
  significant figures that went into the problem.

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Example 1
0.47775

• 14.7 x 0.0325

However how many sig. figs. Can we have?
Three.
What will the correct answer be?
0.478
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Example 2
0.1333223684???

• 101.325 / 760.

However how many sig. figs. Can we have?
Three.
What will the correct answer be?
0.133
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Combined operations

• REMEMBER ORDER OF OPERATIONS
• My Dear Aunt Sally

Each time you switch from mult/div. to add/sub
the rules above take effect for the respective
operation
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Example 3

• (5.809 x 7.34) / (0.0087 - 5.0)

-8.542475908
42.63806
/
-4.9913
/
42.6

-5.0
-8.52
What will the correct answer be?
-8.5
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SI Base Units
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SI -
International system of units

• Revised version of the metric system. Made up
  of seven base units from which all others are
  derived.

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7 Base Units -
m

• Length -

meter
Kg
Kilogram
Mass -
Time -
second
s (lower case)
Electric current -
Ampere
A
Temperature -
Kelvin
K
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7 Base Units (cont)-

• Amount of substance -

mole
mol (lower case)
cd
Luminous intensity -
Candela
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Derived Units -

• Volume -

Cubic meter
m3
(L x w x h)
Liter
L
?
1

?

1 m3 L
mL
1000
cm3
?
1000
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Derived units (cont) -

• Density -

grams / cubic centimeter
g/cm3
grams / milliliter
g/mL
Density is symbolized by the Greek letter ? (rho)
.
The formula is derived by dividing mass / volume.
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Derived units (cont) -
Pa

• Pressure -

Pascal
Atmosphere
Atm
Millimeters of Mercury
mm Hg
101.325 Pa
1 atm
1 Bar
760 mm Hg
14.7 psi
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Derived units (cont) -

• Area -

Square meter
m2
(l x w)
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The Conversion Line-

• A method to help with conversion of one metric
  unit to another.

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K
H
Da
d
c
m
p
?
n
Base unit m, g, L,
To use the above start with the unit you know,
determine how many "places" you must move to get
the unit you desire, then move your decimal in
that direction, that many places.
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K
H
Da
d
c
m
p
?
n
Base unit m, g, L,
Example 1
20.0 mm
?
Km
0.000020
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K
H
Da
d
c
m
p
?
n
Base unit m, g, L,
Example 2
123.0 L
?
mL
123000.
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K
H
Da
d
c
m
p
?
n
Base unit m, g, L,
Example 3
0.454 g
?
mg
454.
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Temperature Relationships and Conversions

• Kelvin (always capitalized)

vs.
Celsius
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K
?C
Boiling of H2O
100
373.15
Freezing of H2O
0
273.15
Absolute Zero
-273.15
0
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K
?C 273.15
Solve for Celsius.
?C
K - 273.15
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Dimensional Analysis-

• A technique used to convert and combine numbers
  with like and different units. This method is
  especially useful to solve "story" problems like
  the ones we will frequently see in Chemistry.

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• This technique simply requires you to "set up"
  and then "multiply and convert" fractions with
  the units that you are working.

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Conversion Factor-

• A ratio, including the units, set up as a
  fraction and used to solve "Chemistry problems.

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Example 1

• 1500 mL ? L

To solve set up as follows
1500 mL
1 L 1000 mL
1.5 L

x
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Example 2
How long is a 1,000,000 seconds (in days)?
1,000,000 11.57 days
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Example 3
According to the National Debt Clock, the
national debt is (visit web site
nationaldebtclock.com) "X" trillion of dollars.
How long until 1 trillion seconds pass?
1,000,000,000,000 sec ?
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