__Significant
Figures Rules__

Recording **significant
figures **(meaningful digits):

1.
In measurement, record as many digits as possible, last one should be
uncertain.

2. Number of recorded digits should reflect
precision of instrument used.

To count significant figures:

1. All nonzero digits are significant.

5.37
has 3 significant figures.

42.93
has 4 significant figures.

2. Zeros between nonzero digits are significant.

106
has 3 significant figures. (It has been
measured to the ones place.)

20.03
has 4 significant figures. (It has been
measured to the hundreths place.)

3. Zeros to the right of the decimal are
significant.

8.00
has 3 significant figures. (It has been
measured to the hundreths place.)

4. Zeros preceding the first nonzero digit are
not significant.

0.002
has 1 significant figure. (0.002 = 2 x
10^{-2})

5. Zeros on the right of the number without a
decimal are not significant.

(Sometimes
you have to use scientific notation to show the proper number of

signficiant
digits.)

200
has 1 significant figure.

200**.** has 3 significant figures.

2.0
x 10^{2} has 2 significant figures.

Significant figures in arithmetic:

1.
Multiplication & division:
answer has same number of significant figures as the number with the
fewest.

258 mi ÷ 5.5 hr
= 47 mi/hr

(258 has 3 significant
figures and 5.5 has 2 significant figures, so the speed has

only 2 significant
figures.)

2.
Adding & substracting: round
off answer to same uncertainty as least certain number.

If you have 3 rocks with
masses of 1.258 g, 3.5 g and 9.41 g, the total mass of

rocks is: 1.258

3.5

__ 9.41 __

14.168

The correct answer is
14.2 g. 1.258 has been measured to the
thousandths place,

3.5 to the tenths place
and 9.41 to the hundredths place, so the answer is only

known to the smallest
place, in this case, the tenths place.

3.
Exact numbers (defined quantities; i.e., not measured) never limit
significant figures.

Since the density of
water is defined as exactly 1 g/cm^{3 }, it can have as many

significant figures as
you want, so the the number of significant figures in a

calculation depends on
the other numbers in the problem.
Similarly, there are

exactly 100 cm in 1
meter.