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<big><font size="2"><big>I'm getting questions about eqn 8 for the
actual density of water<br>
and s.f. in the calculations.<br>
<br>
The eqn on page 8 uses two numbers, -0.00030 and 1.0042.
People<br>
have asked if these are exact. No they aren't. Someone took
temperature<br>
and density data between 20 and 30 C and fit the data to a
linear eqn.<br>
In doing so the sig. fig. for these numbers were determined
from the s.f.<br>
for the temp and density used. You need to use the s.f. in
these numbers<br>
and the s.f. for your temperature to determine the proper s.f.
for the<br>
actual density. This can be rather tricky since you need to
use the rules<br>
for mult/div and add/subtr. in the same calculation (mult.
rule first followed<br>
by add. rule). I can pretty much make assurances you won't
get 1 or 1.0.<br>
Just so all of you know, water has it's greatest density of </big></font></big><big><font
size="2"><big>1.00000 g/mL at<br>
4.0 Celsius. It's density is 1.0 g/mL (two s.f., 1 decimal
place) from 0 C to 100 C.<br>
<br>
You need to report the proper number of s.f. in the table for
all the numbers,<br>
including the error and % error. This applies even if you use
Excel.<br>
<br>
This is the same for your graphs. The s.f. in your density
and intercept<br>
are determined by the s.f. in your mass and volume being
plotted. I will<br>
say since doing a best-fit line averages out the error in your
actual data<br>
points, if you have enough data points you can usually gain
one s.f. from<br>
a graph. For instance, with enough data points, if you had 3
s.f. for<br>
the mass and 3 s.f. for the volume you could report 4 s.f. for
the slope<br>
and intercept. Two or three data points is not enough to gain
a s.f. Why?<br>
think about this from the perspective of plotting a best-fit
line. The purpose<br>
of a best-fit line is to "average out" the error in the data
points. If you have<br>
only two data points the best-fit line will go right through
them and will<br>
not average out the error in the data. Adding one more (total
of 3 data points)<br>
isn't much better. The more data points you have the safer it
is to claim an<br>
extra s.f. in the numbers from the best-fit line (slope,
intercept). For our<br>
purposes in lab we'll say you need at least four.<br>
<br>
Dr. Zellmer</big></font></big>
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