Transcript Scientific Notation

Significant Figures
Using math correctly in science
courses
Significant figures
When performing mathematical
operations in science we round our
answers in a certain way.
 If I have 17 marbles and the entire lot
has a mass of 24.5 g, how much does
each marble weigh? (do it on your calc)

– 1.44118 g? NOT! I can’t report that long
decimal because I don’t have a scale this
accurate!
The Big Picture
We have to round numbers in science
because we can’t lie about our
certainty.
 We have to decide which numbers
“count” in rounding
 This will be confusing at first be patient
you will get it!

Rules for determining if a digit
counts as a significant figure
Non-zero integers (numbers that are
not zero ) always count as significant
figures.
 Three classes of zeros:

– Leading zeros: zeros that precede all
nonzero digits do not count as significant
figures.
– Captive zeros: zeros between nonzero
digits always count as significant figures.
– Trailing zeros: zeros at right end of
nonzero digits count if there is a decimal
point anywhere in the number!
Is there a decimal, really???
In science, if there is not a decimal in
the number you cannot assume one!!!
 For example:

– 2000: uncertainty range of 1500 to 2499
» Range = 999 (2499-1500)
– 2000.: range of 1999.5 to 2000.4
» Range = 0.9 (2000.4-1999.5)
What Counts as a S.F.?

Exact Numbers never count when
determining the number of significant
figures in an answer!
– Get them from counting (number of
people).
– Get them from definitions (1 in. = 2.54
cm).
Rules for rounding using Sig
Figs

For Multiplication and Division
– The answer must be rounded to the least number
of significant figures of any number in the
problem.

For Adding and Subtracting
– The answer must have the same number of
decimal places (or be as precise) as the least
precise number in the problem.
When to round…


Round at the end of the problem or before
switching between the two systems of
multiplication and division, and adding and
subtracting, if both systems are used in the
problem.
Example
–
–
2.4 x 2.0 round at end
(2.4 x 2.0) + 45.78 round between switching
between multiplying and adding.
+
1.28
52.2
3.092
56.572
56.6
0.475
75.
+ 9.0
84.475
84.
275.28
- 258.0
17.28
17.3
100.0
50.072
+ 9.9
159.972
160.0
1) 2.89 x 14.00 = ?
2) 1.75 x 250,000 = ?
3) 18.0 x 0.0013 = ?
4) 25 x 159 = ?
40.5
40.46
440,000
437,500
0.0234
0.023
4.0
x 103
4000
3975
5) 0.0030 x 0.00109 = ?
0.00000327
0.0000033
3.3 x 10-6
6) 25.00  15.0 = ?
1.67
1.66666666
Problems???

Sig Fig Problem Set