Transcript Scientific Notation - Belle Vernon Area School District

OBJECTIVE/WARM-UP
• Students will be able to distinguish between
accuracy and precision.
• Students will be able to use scientific notation.
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How many sig figs in each number?
3.400
0.00304
0.34090
0.0030
4500
NOTES-ACCURACY
Word/Phrase:
accuracy
Definition:
How close the
measurement is to
the real, true, or
correct value
Hints or diagram: Meaning in My
own words:
correctness
NOTES-PRECISION
Word/Phrase:
precision
Hints or diagram:
Definition:
How close measurements
are to each other
Meaning in My own
words:
repeatable

On the TV show “The Biggest Loser”, weight loss is
reported in whole pounds, but percentage weight loss is
given with two decimal places. For example, if a 210 lb.
person lost 4 pounds, the percent weight loss is reported
as 1.90% weight loss. Write a letter to the producers of
the show to explain how this is unfair and not correct
precision in reporting the percentage weight loss.
Suggest a way to correct this for future shows.
Scientific Notation
A short-hand way of writing
large numbers without
writing all of the zeros.
The Distance From the
Sun to the Earth
93,000,000
Large Numbers
Step 1
Move decimal left
Leave only one number in front of
decimal
Step 2
Write number without zeros
Step 3
Count how many places you moved
decimal
Make that your power of ten
The power of
ten is 7 because
the decimal
moved 7 places.
93,000,000 --Standard Form
9.3 x 107 --Scientific Notation
Practice Problem
Write in scientific notation.
Decide the power of ten.
1) 98,500,000 = 9.85 x 10?
3) 279,000,000 = 2.79 x 10?
9.85 x 107
6.41 x 1010
2.79 x 108
4) 4,200,000 = 4.2 x 10?
4.2 x 106
2) 64,100,000,000 = 6.41 x 10?
More Practice Problems
On these, decide where the decimal will be moved.
1) 734,000,000 = ______ x 108
2) 870,000,000,000 = ______x 1011
3) 90,000,000,000 = _____ x 1010
1) 7.34 x
108
2) 8.7 x
1011
3) 9 x 1010
Complete Practice Problems
Write in scientific notation.
1) 50,000
2) 7,200,000
3) 802,000,000,000
1) 5 x 104
2) 7.2 x 106
3) 8.02 x 1011
Scientific Notation to
Standard Form
Move the decimal to the right
3.4 x 105 in scientific notation
3.40000 --- move the decimal
340,000 in standard form
Write in Standard Form
6.27 x 106
9.01 x 104
6,270,000
90,100
Small Numbers
Step 1
Move decimal right
Leave only one number in front of
decimal
Step 2
Write number without zeros
Step 3
Count how many places you moved
decimal
Make that your power of ten
The power of
ten is -4 because
the decimal
moved 4 places.
0.000324 --Standard Form
3.24 x 10-4 --Scientific Notation
Practice Problem
Write in scientific notation.
Decide the power of ten.
1) 0.000000985 = 9.85 x 10?
3) 2.79 = 2.79 x 10?
9.85 x 10-7
6.41 x 10-1
2.79 x 100
4) 0.042 = 4.2 x 10?
4.2 x 10-2
2) 0.641 = 6.41 x 10?
Complete Practice Problems
Write in scientific notation.
1) 0.005
2) 0.000072
3) 0.000802
1) 5 x 10-3
2) 7.2 x 10-5
3) 8.02 x 10-4
Scientific Notation to
Standard Form
Move the decimal to the left
3.4 x 10-5 in scientific notation
000034 --- move the decimal
0.000034 in standard form
Write in Standard Form
6.27 x 10-6
9.01 x 10-4
0.00000627
0.000901
Scientific Notation
Examples
Change from scientific notation
a) the distance from Pluto to the Sun is 5.9×10 12 meters
b) the Milky Way disk radius is 3.9×1020 meters.
c) The speed of light is 3 x 10 8 meters/second.
d) the sun is 1.5x 1011 meters from earth
e) Mass of proton : 1.6726 x 10-27 kg
f) Mass of neutron: 1.6749 x 10-27 kg
g) Mass of electron: 9.10939 × 10-31 kg
Change into scientific notation
h) 0.000 000 000 753 kg. is the mass of a dust particle!
i) A proton has a diameter of approximately
0.000000000001 mm
Quick Review
When adding or subtracting:

Make sure the exponents are the same
and line up the decimal points.
When multiplying:

Add the exponents
When dividing:

Subtract the exponents