Transcript Uncertainty in Measurements and Significant Figures

Uncertainty in
Measurements and
Significant Figures
Group 4
Period 1
Uncertainty in Measurements



always a certain degree of
certainty and uncertainty
measurements always have a
level of uncertainty
Uncertainty depends on the
capabilities of the measuring
device
Review: What does the level of uncertainty depend on?
Rules for Counting Significant Figures




include all the certain numbers plus the
first uncertain number
nonzero integers always count
exact numbers have infinite number of
sig. figs. (1in.=2.54cm.)
exact numbers don’t limit sig. figs in
calculations
Continued

zeros have 3 classifications




leading zeros never count (0.00272sf)
captive zeros always count (7.0323sf)
trailing zeros count with decimals (100.04sf)
trailing zeros don’t count without decimals
(1001sf)
Review: Which type of zeros are considered sig. figs.? Which are not?
Answer: captive and sometimes trailing zeros
Rules for Multiplication and
Division of Significant Figures


the number of significant
figures are limited
according to multiplication
and division
the number of sig. figs. is equal
to the number with the
least amount of sig. figs.
from the problem
Review: If 3.2 is multiplied by 2.71, then how many sig. figs. should there be in
the answer?
Answer: 2 significant figures
Rules of Addition and Subtraction
with Significant Figures


The number after the decimal in the
answer is the same as of a factor with the
least decimals.
Ex:
Review: Solve with correct
number of sig. figs.
6.18-3.125=?
Answer: 3.055  3.06
Rounding off




if the digit following the digit to be rounded is
equal or greater than 5, then the preceding digit
is increasing by 1
if the digit following the digit to be round is less
than 5, then the preceding digit stays the same
necessary to round to have correct number of
significant figures
carry digits to the final result then round
Review: If the number after the digit is greater than 5,
what happens to the number to be rounded?
Answer: the number to be rounded increases by one
Quiz
1)
2)
3)
4)
5)
What does the level of uncertainty
depend on?
0.0670  How many sig. figs.?
(1.408 + 9.273) – 1.6715 = ?
3.2 x 2.17  How many sig. figs. are in
the answer?
Why is it necessary to round in
chemistry?
Answer
1)
2)
3)
4)
5)
The measuring capabilities of the device.
4 sig. figs.
9.0095  9.010
2 sig. figs.
To have the correct number of sig. figs.
References




http://www.google.com
http://invsee.asu.edu/Modules/size&scale/uni
t2/sigfigadd.gif (Showing the rule of adding
with sig. figs.)
http://cdnwrite.demandstudios.com/upload//8000/100/
10/3/18113.gif (Picture shows how to count
the sig. figs.)
http://www.chem.sc.edu/faculty/morgan/reso
urces/sigfigs/index.html (Tutoring on the use
of sig. figs.)