Scientific Notation (MAT306).notebook
October 19, 2014
Scientific Notation
In science, sometimes it is necessary to deal with very
large or very small numbers.
Examples: Distances between planets
Size of bacteria
Scientific notation is a way of expressing these numbers
more easily.
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Scientific Notation (MAT306).notebook
October 19, 2014
Example: The Sun is 150 000 000 km from the
Earth.
In scientific notation, we write this number
as
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Scientific Notation (MAT306).notebook
October 19, 2014
In general,
A number greater
A power of 10
than or equal to 1
- a positive exponent for
and less than 10
large numbers
- a negative exponent for
small numbers
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Scientific Notation (MAT306).notebook
October 19, 2014
How to write a number in Scientific Notation.
a)
Large number
523 000 000
1) Locate the decimal 523 000 000.
2) Move the decimal to create a number between 1 and 10
5.23 000 000
3) Count the number of places the decimal moved ‑ this is your exponent
5.23 000 000.
8 places
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Scientific Notation (MAT306).notebook
October 19, 2014
4) Write the number in proper scientific
notation.
Drop all the zeros,
Positive exponent
keep the rest
for a large number
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Scientific Notation (MAT306).notebook
b)
Small number
October 19, 2014
0.000 000 037
All the steps are the same ...
0.000 000 037
0 000 000 03.7
0.000 000 03 7
8 places
... except
the exponent is negative!
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Scientific Notation (MAT306).notebook
October 19, 2014
Summary
1.
Large Numbers
Scientific Notation
- move decimal to the left
- positive exponent
2.
Small Numbers
Scientific Notation
- move decimal to the right
- negative exponent
3.
Only one number allowed on the left of the decimal.
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Scientific Notation (MAT306).notebook
October 19, 2014
Write these numbers in scientific notation.
a)
205 000
b)
0.0046
c)
9 070 000 000 000
d)
0.000 000 000 073
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Scientific Notation (MAT306).notebook
October 19, 2014
Operations With Scientific Notation
Multiplication
1.
Multiply the coefficients together
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Scientific Notation (MAT306).notebook
2.
3.
October 19, 2014
Multiply the powers of 10
Write the results in scientific notation.
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Scientific Notation (MAT306).notebook
October 19, 2014
Division
1.
Divide the coefficients.
2.
Divide the powers of 10
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Scientific Notation (MAT306).notebook
3.
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Write the results in scientific notation.
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Scientific Notation (MAT306).notebook
October 19, 2014
Sometimes the answers we get are not in scientific
notation and we have to "fix" them.
(too big)
The fix:
Move the decimal one place to the left and add one to
the exponent.
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Scientific Notation (MAT306).notebook
October 19, 2014
too small
The fix:
Move the decimal one place to the right and subtract
one from the exponent.
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Scientific Notation (MAT306).notebook
October 19, 2014
Word Problems
The bedroom of Dave's house is . We know that in 1 cm
there are particles of dust per cubic meter. How many particles of dust are present in the bedroom of Dave's house? 3
particles
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Scientific Notation (MAT306).notebook
October 19, 2014
The speed of light is 3 10 8 meters/second. If the Sun is 1.5 1011 meters from Earth, how many seconds does it take light to reach the Earth? seconds
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