Transcript Significant Figures and Scientific Notation

Significant Figures
Aren’t all numbers important?!?!?!?
Yes, but some are more significant than
others…
Accuracy / Precision
 Accuracy – the agreement between a measured
value and a true value.
 Precision – agreement between several
measurements of the same quantity.
Significant Figures
 A measurement can only be as accurate and
precise as the instrument that produced it.
 A scientist must be able to express the accuracy
of a number, not just its numerical value
Significant Figures
We can determine the accuracy of a
number by the number of significant
figures it contains.
Doing Math with Sig. Figs.
ADDING AND SUBTRACTING:
If you add two numbers together the answer is only as precise as your
least precise number.
Your answer will have only as many digits after the decimal point as your least
Precise number.
Example:
5.46 + 2.0 + 3.1111 = 10. 571
The 2.0 has only 1 significant figure past the decimal, so our answer can only
have 1 digit pas the decimal.
Answer = 10.6
Multiplication and Division with Sig. Figs.
Your answer can only be as precise as your least precise number.
This time we are not just worried about after the decimal, but the least precise
number as a whole.
You answer should have the same number of significant figures as the number
In the problem with the fewest significant figures.
Example:
(3.78 x 4.0001 x 4.5) = 68.041701
The 4.5 only has two significant figures so our answer can only have two.
Answer = 68
Scientific Notation
Helping us write
really tiny
or
really big numbers
Carelessness when using numbers
I have a million math problems to do
 I have a trillion things to get done tonight


If you win 1 million dollars and you’re
given the prize in 100 dollar bills, your
stack of money is….
4 inches high
Rules to Scientific Notation
Parts:
1. Coefficient (mantissa) – must be a
number from 1 – 9.9
2. Exponent – a power of 10
3.4 x 106
Easier than writing 3,400,000
Numbers Greater Than 10
1.
2.
Find the number by moving the decimal
point that is between 1 – 9.9
45,300,000  4.53
Write a positive exponent which is
equal to the number of places you
moved the decimal point to the left.
4.53 x 107
Numbers Less Than 1
1.
2.
Find the number by moving the decimal
point that is between 1 – 9.9
0.000291  2.91
Write a negative exponent which is
equal to the number of places you
moved the decimal point to the right.
2.91 x 10-4
Math Operations & Sci. Notation

For Multiplication:
multiply coefficients
add exponents
(3.0 x 104) x (2.0 x 102) = 6.0 x 106
3x2=6
4+2=6
Math Operations & Sci. Notation

For Division:
divide coefficients
subtract exponents
(6.4 x 106) / (1.7 x 102) = 3.8 x 104
6.4 / 1.7 = 3.8
6–2=4
Be Careful…

Remember the rule about the coefficient!
Ex. (4.0 x 103) x (3.0 x 104) = 12.0 x 107
WRONG!!!
Answer = 1.2 x 108
Math Operations & Sci. Notation

For Addition and Subtraction:
must make the exponents the same
Ex. 5.4 x 103 + 6.0 x 104 =
0.54 x 104
+6.0 x 104
6.5 x 104
Special Note
Sometimes exponents are written
differently.
 We are used to 3.4 x 105
 However, you may see 3.4E5
 It means the same thing (“E” represents
the exponent and replaces x 10

Write in Scientific Notation and
Determine the number of sig. figs.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
0.02
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0.020
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501
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501.0
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5,000
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5,000. _____
6,051.00 _____
0.0005 _____
0.1020 _____
10,001 _____
8040
12. 0.0300
13. 699.5
14. 2.000 x 102
15. 0.90100
16. 90,100
17. 4.7 x 10-8
18. 10,800,000.
19. 3.01 x 1021
20. 0.000410
11.
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