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AP Chemistry: Rules for Significant Figures

Part of the AP Chemistry For Dummies Cheat Sheet

After you get an answer on the AP Chemistry exam, make sure that you provide the correct number of significant figures in your answer. Here is a summary of the rules for assigning significant figures:

  • Any nonzero digit is significant. Thus, 6.42 seconds (s) contains three significant figures.

  • Zeros sandwiched between nonzero digits are significant. Thus, 3.07 s contains three significant figures.

  • Zeros on the left side of the first nonzero digit are not significant. Thus, 0.0642 s and 0.00307 s each contain three significant figures.

  • When a number is greater than 1, all digits to the right of the decimal point are understood to be significant. Thus, 1.76 s has three significant figures, while 1.760 s has four significant figures. We understand that the 6 is uncertain in the first measurement, but is certain in the second measurement.

  • When a number has no decimal point, any zeros after the last nonzero digit may or may not be significant. Thus, in a measurement reported as 1370 s, we cannot be certain if the "0" is a certain value, or if it is merely a placeholder. Be a good chemist. Report your measurements in scientific notation to avoid such annoying ambiguities.

  • Numbers resulting from counting (for example, one kangaroo, two kangaroos, three kangaroos . . .) or from defined quantities (for example, 60 seconds per 1 minute) are considered completely certain. These values are understood to have an unlimited number of significant figures, consistent with their complete certainty.

  • When taking the log of a number, as when calculating pH or pOH from [H+] or [OH], only the decimal portion of the answer applies toward the significant figure count (not the preceding integer). For example, if [H+] = 0.0100M and pH = –log[H+], then pH = 2.000. Why? 0.0100 contains three significant figures. Therefore, the decimal portion of the log answer (the mantissa) contains three significant figures. The preceding integer (the characteristic "2" in this case) does not count toward the significant figure total.

The final thing to burn into your brain about significant figures is that your final answer should always be rounded to the same number of significant figures as the least-precise number you were given in the problem. However, do not round any of the numbers you are given until the very end after you have plugged them into your equations in their full, precise glory.

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