Untitled - Kelly Walsh High School

Chemistry: First Steps 5
exact normally by definition. There are exactly 12 items in a dozen, 36 inches in
a yard, and so forth. Measured values, like the ones you will be dealing with in
lab, have uncertainty associated with them because of the limitations of our
measuring instruments. When those measured values appear in calculations,
the answer must reflect that combined uncertainty by the number of significant
figures that you report in the final answer. The more significant numbers reported,
the greater the certainty in the answer.
The measurements that you use in calculations may contain varying numbers of
significant figures, so carry as many as possible until the end and then round off
the final answer. The least precise measurement will determine the significant
figures reported in the final answer. Determine the number of significant figures
in each measured value (not the exact ones) and then, depending on the mathematical
operations involved, round off the final answer to the correct number
of significant figures. Here are the rules for determining the number of significant
figures in a measured value:
1. All nonzero digits (1, 2, 3, 4, and so on.) are significant.
2. Zeroes between nonzero digits are significant.
3. Zeroes to the left of the first nonzero digit are not significant.
4. Zeroes to the right of the last nonzero digit are significant if there is a decimal
point present, but not significant if, there is no decimal point.
Rule 4 is a convention that we will be using, but some teachers or books may
use alternative methods, so check with your instructor for the convention she or
he would like you to use.
By these rules, 0.320400 would contain six significant figures but 320,400 would
only contain four.
Another way to determine the number of significant figures in a number is to
express it in scientific (exponential) notation. The number of digits shown is the
number of significant figures. For example, 2.305 10 5 would contain four significant
figures.
In determining the number of significant figures you will express in the final
answer, the following rules apply:
1. For addition and subtraction problems, round the answer off to the same
number of decimal points as the measurement with the fewest decimal places.
18.256 cm 7.25 cm 2.7 cm 28.206 cm 28.2 cm (rounded to the
tenths place)