Cliffs AP Chemistry, 3rd Edition

Mathematical Operations

Significant Figures

In order to receive full credit in Section II, the essay section, you must be able to express your

answer with the correct number of significant figures (s.f.). There are slight penalties on the AP

chemistry exam for not doing so. The “Golden Rule” for using significant figures is that your

answer cannot contain more significant figures than the least accurately measured quantity. Do

not use conversion factors for determining significant figures. Review the following rules for

determining significant figures. Underlined numbers are significant.

• Any digit that is not zero is significant. 123=3 s.f.


• Zeros between significant figures (captive zeros) are significant. 80601=5 s.f.; 10.001=
  5 s.f.


• Zeros to the left of the first nonzero digit (leading zeros) are not significant. 0.002=1 s.f.


• If a number is equal to or greater than 1, then all the zeros written to the right of the deci-
  mal point (trailing zeros) count as significant figures. 9.00=3 s.f. The number 100 has
  only one significant figure (100), but written as 100. (note the decimal point), it has three
  significant figures. 400. =3 s.f.


• For numbers less than 1, only zeros that are at the end of the number and zeros that are be-
  tween nonzero digits are significant. 0.070=2 s.f.


• For addition or subtraction, the limiting term is the one with the smallest number of decimal
  places, so count the decimal places. For multiplication and division, the limiting term is the
  number that has the least number of significant figures, so count the significant figures.
  11.01 + 6. 2 + 8.995 =26. 2 (one decimal place)
  32.010 × 501 =1.60 × 104 (three significant figures)

Logs and Antilogs

You will use your calculator in Section II to determine logs and antilogs. There are two types of

log numbers that you will use on the AP exam: log 10 , or log, and natural log, or ln. Log base 10

of a number is that exponent to which 10 must be raised to give the original number. Therefore,

the log of 10 is 1 because 10^1 is 10. The log of 100 is 2 because 10^2 is 100. The log of 0.001 is

−3, and so on.

There are a few types of problems on the AP exam in which you may have to use a natural log-

arithm. The symbol for a natural logarithm is ln. The relationship between log 10 and ln is given

by the equation lnx =2.303 log 10 x.

Part I: Introduction

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