Scientific Notation and
Significant Figures
Video
• Follow the two prompts in your notes while
you watch a short video.
• http://www.youtube.com/watch?v=AWof6knv
QwE
Why use Scientific Notation
• For really big numbers
• For really tiny numbers
How long does it take you to write out
602200000000000000000000
vs.
6.022 x 1023 atoms
Writing in Scientific Notation
Exponent
6.022 x
23
10
atoms
Base
Coefficient
Rules
• The coefficient must be larger or equal to 1
but smaller than 10.
– 1 ≤ coefficient < 10
• The exponent is the number of places the
decimal point must be shifted to give the
number in long form.
Negative Exponent
• The exponent is negative when
– The original number is less than 1.
– Moving the decimal place to the right.
Example:
0.0000042 grams
Positive Exponent
• The exponent is positive when
– The original number is greater than 9.
– Moving the decimal place to the left
Example:
374000000 Liters
In class practice
•
•
•
•
•
•
•
•
3,400 ____________________________________
0.000023 _________________________________
101,000 __________________________________
0.010 ____________________________________
45.01 ____________________________________
1,000,000 ________________________________
0.00671 _________________________________
4.50 ____________________________________
Reverse! Write in “regular” notation.
•
•
•
•
3.19 x 10 -4
5 x 106
1.34 x 102
3.702 x 10-3
Adding and Subtracting with numbers
in Scientific Notation
(4 x 108) - (3 x 106) =
• Step 1: Make the exponents the same
(4 x 108) – (0.03 x 108) =
• Step 2: Add or subtract the coefficients
4 – 0.03 (x 108) = 3.97 x 108
• Step 3: If necessary put the answer back in
scientific notation
Multiplying with Numbers in Scientific
Notation
•
•
•
•
Step 1: Multiply the coefficients
Step 2: Add the exponents together
Step 3: Put it all together
Example:
(2 x 103) x (3 x 104) =
Step 1:
( 2 x 3) = 6
Step 2:
(3 + 4) = 7
Step 3:
6 x 107
Dividing with Numbers in Scientific
Notation
•
•
•
•
Step 1: Divide the coefficients
Step 2: Subtract the exponents
Step 3: Put it all together
Example
(8 x 104) / (2 x 106)
Step 1:
(8/2) = 4
Step 2:
(4-6) = -2
Step 3:
4 x 10-2
Practice
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•
•
•
•
(3.2 x 10-5) x (3 x 104) =
7. (6.0 x 102) x (7.0 x 104) =
8. (2.4 x 10-1)/ (4.0 x 10-3) =
(8.0 x 105)/ (4.0 x 103) =
(5.0 x 104) + (3.0 x 104) =
(2.4 x 10-1) - (4.0 x 10-3) =
Easier Way…
• In your calculators use either:
– The “EE” key
–^
Significant Figures
• How are gas prices listed at the pump?
– Why is this done?
– Does it affect how much you pay?
What are significant figures?
• All digits of a measured quantity, including the
uncertain one.
• The greater the number of significant figures,
the greater the certainty of the measurement.
How do we determine if the digits are
significant?
• If something was counted, it is not significant.
• Only measurements, have significant digits.
Pacific to Atlantic Rules
• Think of the number as the United States,
then look for a decimal point
If a decimal point is PRESENT then start at the
“Pacific” side.
If a decimal point is ABSENT then start at the
“Atlantic” side.
2.3006
Pacific
Atlantic
Decimal Point Present
• STEP 1: Start at the 1st nonzero number
• STEP 2: Count all the way to the “Atlantic” –
no exceptions
Examples
•
•
•
•
100.21
0.000453
12.8
0.00709
Decimal Point Absent
• STEP 1: Start at 1st nonzero
• STEP 2: Count all the way to the Pacific – no
exceptions
Examples
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•
•
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15630
8004
10
950360010