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Significant Figures
There are two kinds of
numbers:
 Exact
 Inexact
Example: There
are twelve eggs
in a dozen
Example: Any
measurment
If I were to measure a piece
of paper,
I might get 220 mm
 If I am more precise, I might get 216
mm.
 An even more precise measurement
would be 215.6 mm.

Precision vs. Accuracy
 Accuracy
 Precision
- Refers to how
- Refers to how
closely individual
measurements
agree with each
other
closely a
measured value
agrees with the
correct value
In any measurement, the number
of significant figures is the number
of digits believed to be correct by
the person doing the measuring.
It also includes one
estimated digit.
Here are 3 examples of when
sig. figs. are important when
measuring volumes in the lab.
A
beaker
A
graduated cylinder
A
buret
A rule of thumb:
Volumes should be read to 1/10
of the smallest division.
Example: If the smallest division
is 10 mL, the volume would be
read as having an error of 1 mL.
A Beaker
The smallest division is
10 mL-so we can read
the volume to 1 mL.
 The volume in the
beaker is 47(+ or –)
1mL. It might be 46-it
might be 48.
 So, how many sig.
figs.????
 (2) - The “4” we know
for sure, plus the
“7” that we had to

estimate.
A Graduated Cylinder





The smallest division is 1 mL
so we can read the volume to
0.1 mL.
The volume could be read as
36.5 (+ or -) 0.1 mL.
The true volume could be
36.4 or 36.6.
How many sig. figs???
(3)- The “3” and “6” we know
for sure- the “5” had to be
estimate.
Conclusion:
Significant figures
are directly linked
with measurement.
Determining the number of
sig. figs. in a number.
Picture a map of the U.S.
 If a decimal point is present, count
from the Pacific side.
 Start counting with the first nonzero
digit.
 All digits from here to the end,
including zeros, are significant.

Examples:
 0.00682
Answer: 3
1.0
Answer: 2
60.
Answer: 2
 1.0 x 102
Answer: 2
 If
the decimal point is absent,
start counting from the
Atlantic side.
 Start with the first nonzero
digit.
 All digits from here to the end,
including zeros, are significant.
Examples:
 60
Answer: 1
603
Answer: 3
6030
Answer: 3
Sig Figs Practice Problems
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
100.00 K
1051 g
1100 kg
0.0000005 s
0.0700 m
3000.59 mL
500,000 g
1,562,003,000,000 kg
245 s
0.00000005200 m
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
24.0 K
1.05 g
0.032 kg
2300.7 s
17.050 m
30080 K
607 g
1.0000005600 kg
780 s
700,000 m
Significant Figures in Calculations:
Rules for Multiplication and Division
The answer contains no more
significant figures than the
least accurately known number.
Examples:
The number with the
least # of sig. figs. has
2 sig. figs. Therefore, the
answer must have 2.
The number with the least
# of sig. figs. has 3 sig.
figs. Therefore, the
answer must have 3.
Rules for Addition and Subtraction
The number of sig. figs. is
determined by the location of digits
in the number with the largest
uncertainty, not the number of
significant figures in the number.
Examples:
The least precise number
is 2.02. It has sig. figs.
out to the hundredths
place. Therefore the
answer will have sig. figs.
out to the hundredths
place.
The least precise # (1.0236)
has decimals carried out 4
places. Therefore the
answer will have sig. figs.
carried out 4 decimal places.