# The number of significant figures is equal ```H2: SIG FIG RULES SUMMARY

page 1
The number of significant figures is equal to the number of certain digits plus
one uncertain digit. For example:
2
2.05
2.10
2.15
The above scale would be read as 2.097, with the underlined digits being
characterized as “certain,” and the 7 in the thousandths place being
characterized as “uncertain.” The total number of significant figures would be
4 (SF = 4).
Rules for determining sig figs with zeroes

Zeroes to the right of the decimal are only significant if there are non-zero
digits in front of them (to the left):
0.0035  SF = 2
1.0035  SF = 5
13.00  SF = 4

Zeroes to the left of the decimal must be surrounded by non-zero digits in
order to be significant:
3000  SF = 1
3003  SF = 4

If you have a number such as 3000 for which you want to convey SF = 4, it
must be written in one of the following ways:
3.000  103 or 3000. (Note the decimal point in the latter.)
H2 SIG FIG RULES SUMMARY
page 2
SIG FIG rules for multiplication and division operations:

Look at the numbers on which you are operating. Count up the number of sig
figs in each. If one of the numbers has fewer sig figs than the other numbers,
that number of sig figs will be the same number of sig figs in your answer.
You must then perform the operation and round the result to the correct
number of sig figs:
29.35  43.678 = 1281.9493

SF=4


 1282 (SF=4)
SF=5
Exact numbers (things which can be counted, as opposed to being
measured), such as 6 beakers, or a dozen rolls, have an infinite number of sig
figs. Thus, when they are used in a calculation with a measured value, the sig
figs associated with the measured value will determine the number of sig figs:
6 beakers  43.753

g
= 262.52 g (rounded to SF = 5)
bea ker
SIG FIG rules for addition and subtraction operations:
Look at the numbers on which you are operating. For each number, count up
the number of digits to the right of the decimal. The number with the fewest
number of digits to the right of the decimal will determine the sig figs for the
answer. The number of digits to the left of the decimal is unimportant. That is,
if the number having the fewest digits to the right of the decimal has 2 digits
after the decimal, the answer will have 2 digits after the decimal:
23.6374  4 digits to the right of decimal
+3.76__  2 digits to the right of decimal
27.40
 SF = 4, rounded to 2 digits to the right of the decimal
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