Performing these
conversions is a lot like
going on a road trip.
Scientific Notation
Scientist use special notation to express very
large or very small numbers.
Example I: 300,000,000 g can be written as…
3 x 108 g
Ex II: 1,007,000,000 sec can be written as…
1.007 x 109 sec
Ex III: 0.000 000 000 004 76 mL can be written as…
4.76 x 10-12 mL
Significant Figures
Atlantic - Pacific Rule:
Decimal Present: Count from the Pacific side
Decimal Absent: Count from the Atlantic side
Start counting at the first non-zero number and
count until you reach the end of the number
Ex. I: 3.00700
Decimal Present… Pacific (left)… 6 sig. figs.
Ex. II: 300,700
Decimal Absent… Atlantic (right)… 4 sig. figs.
Before we take this trip, let’s
review significant figures…
Determine how many significant figures are in
each of the following measurements.
1)
2)
3)
4)
5)
6)
0.0034050 L
33.600 m
7500.0 g
47,900 mm
7,000,000,001 miles
8.07 Hz
5
___________
5
___________
___________
5
3
___________
10
___________
___________
3
More practice…
Round the following measurements off so that
they each contain 3 significant figures.
7) 366.2 L
8) 9,047,022 mg
9) 12.76 g
10) 999.9 J
___________
366 L
9,050,000
mg
___________
___________
12.8 g
1.00 x 103 J
___________
Notice this one must be in scientific
notation to have 3 sig. figs.
Significant Figures in Calculations
When multiplying and dividing, limit
and round to the least number of
significant figures in any of the
factors.
Example:
23.0 x 432 x 19 = 188,784 = 190,000
The answer is expressed as 190,000 or
1.9 x 105 since 19 has only two sig. figs.
Significant Figures in Calculations
When adding and subtracting, limit and
round your answer to the least number of
decimal places in any of the numbers
involved in the calculation.
Example:
123.25 + 46.0 +86.257 = 255.507 = 255.5
The answer is expressed as 255.5 since 46.0
has only one decimal place.
Before we take this trip, let’s
review significant figures…
Perform the prescribed operations. Round your
answers to the proper # of sig. figs.
11.4 m/s
11)36.57 m / 3.21 s =
___________
97.6 g
12)41.376g + 13.3g + 42.9g=___________
76.2 m2
13)5.67 m x 13.44 m
___________
1.0 m/s2
14)(5.83 m/ 2.67 s) /2.1 s
___________
60 V
15)9.374 V x 6
___________
From now on, we will round all our answers
to the correct # of significant figures.
Now back to our road trip…
Let’s say you want to travel from Oracle Jct to
Casa Grande...
You must travel
through Tucson…
a two part trip.
Rule: You must stay on the roads
Rule: You need a map. Sometimes the map can
be in your head. But, not at first.
OK…Lets talk about making
maps and solving conversion
problems. The method we use
is called the “Factor-Label”
method, a.k.a. dimensional
analysis.
Given 1 kildurkin = 18 gallons
For Example:
gallons
kildurkins
This is our map.
For Example:
Given 1 kildurkin = 18 gallons
gallons
kildurkins
How many kildurkins is 14 gallons?
14 gallons
1 kildurkins
18 gallons
=0.78 kildurkins
General Format...
given
going to
coming from
Let’s expand the map...
Also given: 2 farkins = 1 kildurkin
gallons
kildurkins
farkins
Also given: 1 hogshead = 63 gallons
1 barrel = 3.3 bushels
hogshead
1 bushel = 8 gallons
gallons
bushel
barrel
kildurkins
farkins
Now, Lets solve a problem.
How many hogsheads are 14 barrels?
Finish Here
The trip will require 3
hogshead
transitions
3
gallons
kildurkins
farkins
2
bushel
1
barrel
Given: Start Here
How many hogsheads are 14
barrels?
hogshead
Given
3
gallons
14 barrels 3.3 bushels 8 gallons
1 barrel
1 bushel
1 hogshead
63 gallons
= 5.9 hogsheads
2
bushel 1
going to
going to
going to
coming from coming from coming from
barrel
Now you try one. How many farkins is
3.00 bushels?
End Here
hogshead
gallons
kildurkins
farkins
Start Here
bushel
barrel
This will require 3
Conversions.
bushels
gallons
farkins
kildurkins
3.00 bushels 8 gallons 1 kildurkin
2 farkins
1 bushel
1 kildurkin
18 gallons
= 2.67 farkins
Wow! How
Cool Is That!