SLU CHEM 107-001
Summer 2017
Dr. Eric C. Booth
Lecture 3: density, word
problems, scientific notation
Density
 Amount
of material (mass) that fits
into a given space (volume)
 Constant for any ‘pure’ substance
 Units: g/cm3, kg/m3, g/L, …
 Density proportional to mass, IF
volume remains constant
 …BUT
density NOT same as mass!
 which is more dense…1.00 kg of bricks, or
100. kg of feathers?
Density
 Density
inversely proportional to
volume, IF mass remains constant
 …BUT
density NOT same as
1/volume!
 Which is more dense…1.00 m3 of
water, or 100. m3 of water?
Density: Example
I
have 100. grams of Hg (density =
13.6 g/cm3), and 100. grams of
gasoline (density = 0.900 g/cm3).
 I put the gasoline in one beaker,
and the mercury in another beaker.
 Each beaker is just big enough to
hold its liquid without overflowing.
 Which beaker is larger? Why?
Density: Example
Multiple Conversion, Word
Problems
A
diabetic consumes 20.5
exchanges (ex) of carbohydrate
per day. If this diabetic requires
0.700 units (u) of insulin per
exchange, how many units of
insulin will this person use in
one regular, non-leap year (yr)?
Multiple Conversion, Word
Problems
ex  0.700 u  365 d 
u
20.5 
  5240

d  1 ex  1 yr 
yr
Multiple Conversion, Word
Problems
ex  0.700 u  365 d 
u
20.5 
  5240

d  1 ex  1 yr 
yr
Scientific Notation
 Calculations
often involve very
large, very small numbers
 Long numbers hard to understand
 Separating out powers of ten
makes numbers manageable
Standard Numbers in
Scientific Notation
 Given
a number—say, 13,400,000—
we need to break it into two parts:
a
coefficient (specific size)
 a power of ten (general size)
 The
coefficient is always written as
a decimal number, and must be
between one and ten (why?)
Standard Numbers in
Scientific Notation
• This means we have to figure how
far to move the decimal point, to
get a number between one and ten
• In our example:
13,400,000
7 6 5 4 32 1
Standard Numbers in
Scientific Notation
• The number of times the decimal
point gets moved is the power of
ten the coefficient is multiplied by
• Since we moved the decimal point
7 times in our example,
13,400,000
7 6 5 4 32 1
Standard Numbers in
Scientific Notation
• The number of times the decimal
point gets moved is the power of
ten the coefficient is multiplied by
• Since we moved the decimal point
7 times in our example,
1.34 x
7
10
Scientific Notation in
Standard Numbers
• Two cases:
–positive powers of ten
–negative powers of ten
• For a positive power of ten,
multiply the coefficient by that
number of tens
8.6 x
3
10
= 8.6 x 10 x 10 x 10
= 8600
Scientific Notation in
Standard Numbers
• For a negative power of ten,
divide the coefficient by that
number of tens
5.4 x
-2
10
= 5.4 / (10 x 10)
= .054
Prefixes
 Increase,
decrease units’ size by
powers of ten, usually 103 or 10-3
 Exceptions:
(d) = 10-1  deciliter
 centi (c) = 10-2  centimeter
 deci
 Prefixes
increasing size usually
capitalized…
 …except kilo (k) = x 1000: kilogram
 Other, lowercase prefixes decrease
size
Prefixes
 Added
to units to increase or
decrease
their
size by1 factors
of 10
tera
T
one trillion
000 000 000 000
ten
12
pico
p
one trillionth
0.000 000 000 001
10-12