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After one has made measurements in an experiment and done calculations, one must decide how many significant figures to retain in the final reported result. The broad general principle governing this decision is that the final result should convey to the reader the maximum amount of information derivable from the experimental measurements and no misinformation.
This concept is called significant figures. All the digits that one can measure and reasonably estimate are significant. They have meaning and give the reader a sense of how precise the experiment was.
Remember that the last significant digit is somewhat uncertain. This is the case when measured quanties are reported; the last significant digit is a carefully considered estimate by the experimenter and represents the limit of his or her ability to measure, given the measuring instrument being used and the conditions under which the measurement is made. This uncertainty carries over into the result calculated from the measurements. Thus the number of significant figures in a quantity is the number of trustworthy figures in it, the last trustworthy figure being somewhat in doubt (but still useful), because it is based upon an estimation.
Remember that it is the act of measuring that gives significance to a number. Each and every significant figure comes from one of two places. The first is from the divisions enscribed on the measuring scale used. The second source of significance is the experimenter bringing all of his or her experience and training to bear and making a reliable estimate.
Since the instrument's measuring scale is not always available to inspect, there have been rules developed to identify which of the digits in a number is significant and which are not. That is the subject of the next lesson. Pay close attention to the rules and learn them well. The ChemTeam uses them for the remainder of the course and ChemTeam students are deducted points for failure to adhere to significant figure rules.
It is more than likely your teacher acts the same.
Sig Fig Rules is the next lesson to go to.