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Mathematical Functions and Significant Figures
Often, ma th is required using numbers of various significant figures. We’ll cover
only two basic classes of mathematical functions:
(1) Addition and Subtraction: When adding or subtracting two or more numbers,
do not worry so much about the number of significant figures. Instead, keep only the
smallest number of digits after the decimal point that are significant in any of the
numbers. For instance, when adding 101.2336 and 207.44, the answer will have only two
places past the decimal point (308.67).
(2) Multiplication and Division: When multiplying or dividing, keep only the
maximum number of significant figures as is in any of the digits involved. For example,
101.2336 has 7 significant figures, but 207.44 has only 5 significant figures, so our
product can have only 5 significant figures (21,000.).
Be careful not to confuse exact numbers for inexact. For example, we know there
are 12 inches in 1 foot, so if we are using this conversion factor to convert 3.0252 ft to
inches, we might think we can only have two significant figures because of the factor
“12.” However, this is an exact definition, and as such, it can have as many significant
figures as we want. In other words, even though we don’t bother writing the zeros, there
are really “12.000000000000000…” inches in 1 foot because this is an exact definition.
Thus, our answer will be 36.302 inches (5 significant figures).
There are two types of instruments; analog and digital. Digital instruments are
easy, just write down every number they give you, including zeros. This automatically Dakota State University page 230 of 232 Significant Figures General Chemistry I and II Lab Manual gives you the number of significant figures. However, analog devices are a little more
Analogue devices have some form of scale, with an indicator. In an old-fashioned
thermometer, the scale is on the side, with the indicator being the level of the liquid.
Other instruments, like voltmeters, for example, had a scale (usually with a portion
mirrored so you always look at it from the same angle by lining up the pointer so you
cannot see the image) with a pointer. Whenever you have an instrument like this, you
can always estimate one significant figure more than the scale on the instrument.
Take the following example; suppose you
are measuring the liquid in a graduated cylinder,
with markings every 0.1 mL, as shown in the figure
to the left. We know that the liquid level is above
8.7, but less than 8.8; so what is it? (Forgive the
squiggly line; it was drawn by hand.) Well, how far
up does it look to you? Maybe 70% of the way?
OK, so y record 8.77 in your records. Don’t
worry that the las...
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