Transcript Presentation

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 20.15 mm
 You might get 20.14 mm.
 Somebody else may get 20.16

Who is right ?????
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
Remember..there is uncertainty in all
measurement but the precision is
determined by the measuring device.
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.
A Buret





The smallest division is 0.1 mL
so we can read the volume to
0.01 mL.
A good volume reading would be
20.38 (+ or -) 0.01 mL.
An equally precise answer would
be 20.39 or 20.37.
How many sig. figs.????
(4)- The “2”, “0”, and “3” we
know for sure, the “8” we had to
estimate.
Conclusion:
Significant figures are
directly linked with
measurement.
Now, how do we determine
significant figures?
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
Significant Figures in Calculations:
Rules for Multiplication and Division
The answer contains no more
significant figures than the
lease 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.