Significant Figures Review and Other Tips
A. Rules for establishing the number of significant figures (a.k.a. sig figs or sf) in a measurement:
1. Sig figs apply only to measured quantities.
Scientific definitions have an infinite number of sig figs.
Example: 1 min = 60 seconds is a definition, therefore there are as many sig figs as you need in this
conversion.
2. All nonzero digits are significant.
Ex: 287.31 g (5 sf)
3. Regarding zeroes:
a) Zeroes between digits within the number are always significant.
Ex: 240.03 g (5 sf)
b) Leading zeroes are only placeholders. Always (starting from the left) begin with the first non-zero
digit.
Ex: 0.00452 g (3 sf)
c) “Trailing zeroes” with an expressed decimal are always significant.
Ex: 12.0 m (3 sf); 0.1200 L (4 sf); 150. (3 sf)
d) “Trailing zeroes” without an expressed decimal are confusing! (especially in texts)
Ex: 8000 (??? sf) To avoid ambiguity, rewrite the number in scientific notation.
Ex: 8000 ==> 8 x 103 (1 sf) or 8000 ==> 8.0 x 103 (2 sf)
Notice that the magnitude of the exponent is irrelevant in determining the # of sf.
B. Sig Figs in Calculations
1.
When multiplying or dividing, the factor with the least number of sig figs determines the number
in the final answer.
Ex: (2.0 x 10-8 m)(6.4278 x 103 m) = 12.86 x 10-5 m2 = 13 x 10-5 m2 =1.3 x 10-4 m2
Ex: 8.222 x 10-10 = 2.06 x 10-20 = 2 x 10-20
4 x 1010
2. When adding or subtracting, line the numbers up first by the decimal point. (Make sure you have
all of the numbers expressed to the same power.) Decimal places are the key in adding and
subtracting. The answer can have only as many decimal digits as are in the number with the least
significant decimal digits when they are all lined up and have the same exponent of 10.
Ex:
0.124 cm
Ex:
6.2 x 10-2
62. x 10-3 cm
-3
800.4
cm
8.6 x 10 ==>
8.6 x 10-3 cm
___6.52 cm
70.6 x 10-3 cm
807.044 cm
70.6 x 10-3 cm


807.0
cm
71 x 10-3 cm => 7.1 x 10-2 cm
3. In logs, begin counting the first sig fig to the right of the decimal. Numbers to the left relate to the
exponent. Thus the number of sig figs in a number equals the number of digits to the right of the
decimal in the log form. Log N = x or
10x = N
Ex: log 2.0 x 105 = 5.30


2 sf
2 sf
or the antilog of 4.48 = 3.0 x 104
 
2 sf 2 sf
C. Rounding
When rounding, use the odd-even rule.
If the digit after the last significant digit (digit to be rounded) is less than 5, the digit stays the same.
If the digit after the last significant digit is larger than 5, round up.
If the digit after the last significant digit is 5 followed by anything except all zeroes, round up.
If digit after the last significant digit is 5 followed by nothing or all zeroes,
Round up if the previous digit was odd.
Leave digit unchanged if previous digit was even.
(Final rounded digit in this case will always end up even.)
Ex: Round each of these numbers to the tenths place:
6.041 =>
6.0
6.084 =>
6.1
6.050 =>
6.0
6.054 =>
6.1
6.150 =>
6.2
D. Estimating Logs
Remember Log N = x or 10x = N or antilog x = N
Given either x or N you can find the other (to two decimal places) without a calculator with the help
of this little chart. Look up or remember log 2.0 and log 3.0. Then fill in the rest of the chart. Keep
in mind that log 4.0 = log (2.0 x 2.0) = log 2 + log 2. Also, since 5.0 and 7.0 are prime numbers,
you will just have to estimate those by looking at the pattern of the other numbers. Remember, logs
of products are added and logs of quotients are subtracted.
log 1.0 = __________
log 2.0 = __________
log 3.0 = __________
log 4.0 = __________
log 5.0 = __________
log 6.0 = __________
log 7.0 = __________
log 8.0 = __________
log 9.0 = __________
log 10.0 = __________
Ex: log 0.010 = log 1.0 x 10-2 = -2
Ex: log 0.030 = log 3.0 x 10-2 = log 3.0 + log10-2 = (0.48) + (-2) = 1.52
Ex: if log N = -3.70, then N = 10-3.70 = 10(0.3-4) = 100.3 x 10-4 = 2.0 x 10-4
E. To solve quadratic equations, use the formula after rearranging so that all the factors are set equal to
zero.
For the equation ax2 + bx + c = 0
x
 b  b 2  4ac
2a
F. When using algebraic variables, clearly state what x = at the beginning of the problem. It will help
you reassign units to your answer at the end!
G. Lastly, always try to estimate your answers. It may take a few seconds longer, but it can save some
horrible errors! It is very easy to punchy a number into a calculator incorrectly, or you may have set
up the problem incorrectly. (i.e., ask yourself, does my answer make sense?)