9/11/2015
Scientific Notation
Way to simplify BIG
and small numbers
Scientific Notation
Coefficient x 10
exponent
602000000000000000000000 can be
6.02 x 1023
coefficient
exponent
Scientific Notation
Coefficient x 10


exponent
Coefficient MUST be between 1 and 9
Exponent can be either positive or
negative
+ exponent  large # (> 1)
- exponent  small # (< 1)
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9/11/2015
Scientific Notation
Convert the following into
of scientific notation
3.5893 x 10
35893 = ____________
4
Your turn!
5.48 x 10
0.00548 = ___________
-3
1.025 x 10
10.25 = ___________
1
Scientific Notation
Convert the following out
of scientific notation
25790
2.579 x 104 = ________
0.00008647
8.647 x 10-5 = ________
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9/11/2015
Dimensional Analysis
Used to convert between
units
You need to use a
conversion factor
Conversion Factor
Ratio equal to “1”
Contains the unit that you
currently have and the unit
that you want to convert to
Examples:
12 inches = 1 foot
12 inches
1 foot
OR
1 foot
12 inches
60 seconds = 1 minute
1 minute
60 seconds OR
60 seconds
1 minute
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9/11/2015
Dimensional Analysis
Conversion
X

Unit that
you have
Unit that
you want
Unit that
= You want
Unit that
you have
T-diagram
Conversion
Factor
Single-step conversions
30 seconds = ? minutes
30 seconds 1 minute = 0.5 minute
60 seconds
Example #2
How many inches are in 3.7
feet? (12 inches = 1 ft)
3.7 ft
12 in
= 44 in
1 ft
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9/11/2015
Multi-Step Conversion
The conversion factor does NOT
contain both the unit that you have
and the unit that you want.
The unit conversion requires
multiple (more than one) steps.
Example #1
How many km are there in 34,562 cm?
Conversion factors: 100 cm = 1 m
1000 m = 1 km
34,562 cm
1m
1 km
100 cm
1000 m
=
= 0.34562 km
You can do this!
How many minutes are in 2 days?
(given)
2 days
5
9/11/2015
You can do this!
How many minutes are in 2 days?
(given)
2 days 24 hours 60 minutes
(given)
1 hour
1 day
= 2880
minutes
BUT… since there is only 1 digit in the given, there can
only be 1 digit in the answer so…
= 3,000 minutes
Last one smarty pants!
How many seconds are in 2 decades?
Last one smarty pants!
How many seconds are in 2 decades?
2 decades
10 years
365.25 days
1 decade
1 year
24 hours 60 minutes 60 seconds
1 day
1 hour
1 minute
= 631,152,000 seconds
BUT… since there is only 1 digit in the given, there can
only be 1 digit in the answer so…
= 600,000,000 seconds
Now in scientific notation…
= 6 x 108 seconds
6