Week 1
Scientific Notation and Experimental Error
•
In order to avoid writing out lengthy numbers, we use scientific notation.
o
Example 1: Avagadro’s number: 602,214,200,000,000,000,000,000 = 6.022142
X 10
23.
o
Example 2: 0.000032 = 3.2 X 10
5
o
What did we do?
We moved the decimal point to just before the first number, and then
showed how many multiples of 10 are needed to achieve the actual
number.
If you move the decimal point to the right, the sign of the exponent will
be (). This makes sense because it’s like dividing by that many multiples
of 10 to get to your number.
If you move the decimal point to the left, the sign of the exponent will be
(+). This makes sense because it’s like multiplying by that many
multiples of 10 to get to your number.
•
Scientific measurements can be measured with a high degree of certainty to a point, and
then can become uncertain. There are mathematical tools in order to reduce this
uncertainty, or experimental error.
o
Precision
: degree of agreement in a collection of experimental results and is
estimated by repeating the measurements under conditions as nearly identical as
possible.
o
Accuracy
: how close your data is to the “correct” set of data.
o
Random error
: If the multiple repeated experiments are truly identical, then any
differences in results are due to random error.
o
Mean/Average
: sum of all values/ number of values
o
Standard Deviation
: essentially shows how spread out the
various data points collected are, which can decrease your
errors, by allowing you to see and exclude outliers.
•
Significant Numbers number of digits used to express a measurement or calculated
quantity.
o
This EXCLUDES numbers that precede the first nonzero digit.
Ex: 0.000345 has 3 significant digits
o
This INCLUDES numbers (even zeros) that follow the first nonzero digit.
Ex. 643.00 has 5 significant figures.
o
Following addition or subtraction, round off the result to the LEFTMOST
decimal place that contained an uncertain digit in the original numbers.
Ex: 654.
0
+ 0.5
2
= 654.52, but with accounting for sig figs: 652.5.
o
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 Spring '08
 FELKER
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