significant digits.
This number is N.
Now perform the computation and
round the result to N + 2 places. The last digit will be off by an amount
generally less than five points, which is a reasonable value. For example,
multiply the approximate figures 23.12 times 0.12.
5.
OBSERVATIONS AND DATA.
a. General.
In most cases, measurement involves the making of
observations of some sort, and since observation is one place where the
human element enters the picture, it is necessary, therefore, to understand
all of the factors that influence the making of observations and the
recording of data.
b. Observation. Let us assume that at a given time and under a given
set of conditions, a certain standard cell has some true potential between
its terminals, which we shall call Vt.
For several reasons, Vt cannot be
measured exactly. First, the true voltage could be indicated on paper only
by using an infinite number of decimal places and there is no instrument
with that degree of accuracy or precision.
Second, beyond some decimal
place - perhaps the ninth decimal place - the voltage would be constantly
varying due to molecular motion within the standard cell and electron flow
in the lead wires. Third, no matter how sensitive the measuring device, all
measurements affect the energy content of the thing being measured to some
small extent and hence tend to change it so that the measured value is
always different from what it was in the absence of the measurement. Let us
assume that we have a very sensitive and accurate voltmeter, so sensitive,
in fact, that when different readings are made, there is a spread among
them. Disregarding, for the time being, the systematic errors (temperature,
parallax, instrument error, etc), and the loading effect, we still have the
problem of deciding which of our carefully made readings is the "best"
reading.
A simple approach would be to say that the average of five
readings is a better guess than any of the readings taken at random (or
selected from the center of the distribution). Another approach would be to
assume that of the total of all possible carefully made readings, the five
readings constituted an adequate sampling. A sampling is considered to be
adequate to the degree to which its average agrees with the average of the
group from which it was drawn.
It is easy to see that the greater the
spread of the readings taken, the larger the sample must be in order to be
adequate. It is also obvious that some point will be reached in the size of
the sampling, where the gain in accuracy is not worth the effort required to
reach it.
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