Transcript 5.2 Uncertainty in Measurement and Significant Figures Period 5

Period 5
Group# 4
• A measurement always
• Why is the last digit
has some degree of
uncertainty.
• Certain numbers are
always the same and
accurate.
• Uncertainty depends on
the tool used for
measuring.
called an uncertain
number?
• Solution: The last digit is
usually estimated and
can vary.

http://cyberbridge.mcb.harvard.edu/images/math2_1.png

http://cyberbridge.mcb.harvard.edu/images/math2_2.png
•
In the first ruler, it does not include the centimeters, so
measuring the leaf’s length would have to be estimated
causing it to be inaccurate.
•
In the second ruler, it includes the centimeters, so
measuring the leaf’s length is more accurate than using
the first ruler.
• Significant Figures - The
certain digits and the first
uncertain digit of a
measurement.
• Any measurement that has
an estimate is uncertain.
•
Rules
Leading zeroes - are
never significant
b. Captive zeroes - are
always significant
c. Trailing zeroes - are
sometimes significant
a.
 Why do we use significant figures?
Solution: Significant figures allow us to
signify the degree of certainty for a
measurement.
http://online.redwoods.cc.ca.us/instruct/milo/1/sl
d042.jpg
The uncertainty in the last number of a
measurement is usually either +1 or 1.
For example: 3.56 could have been 3.54
or 3.57.
1. If the digits to be removed is
a. less than 5, the preceding digit stays the same.
b. equal to or greater than 5, the preceding digit is increased
by 1.
2. Carry extra digits through to the final result and then
round off.
• Rounding up example:
Round 0.0876 to the
nearest tenth.
• Round down example:
Round o.246 to the nearest
tenth.
• Answer: 0.1 because 8 is
above 5 so you round up
0 up to 1.
• Answer: 0.2 because 4 is
below 0 so it stays the
same.
 Rules: The number of significant figures used when
multiplying is equal to the factor with the least
significant figures.
 Ex: 8.315 / 298 = 0.0279027  2.79 x 10-2
There are three significant figures in this case because
298 has three, which has less sig. figs than the other
factor, 8.315.
• Explanation: 1.6 is the
limiting term in this case
which only has 2 sig. figs,
so the answer will end up
with 2 sig. figs.
http://www.astro.washington.edu/courses/labs/clearinghouse/la
bs/Scimeth/images/multiply.gif
• Explanation: 45.2 is the
limiting term in this case
which has 3 sig. figs, so
the answer will end up
with 2 sig. figs.
http://www.astro.washington.edu/courses/labs/clearinghouse/lab
s/Scimeth/images/division.gif
 Rules: The limiting term is the one with the smallest
number of decimal places for addition and subtraction
which determines the number of decimal places that
are sig. figs for the result.

0.72 - limiting term
+0.0429
0.7629  0.76
There are 2 significant
figures because there are
2 decimal places in 0.72.
 Explanation: 2.02 is the
limiting term because it
has the least decimal
places, so the result will be
ending with 2 decimal
places, 8.04.
http://www.astro.washington.edu/courses/labs/clearinghouse/la
bs/Scimeth/images/addition.gif
 Explanation: 1.0236 is the
limiting term because it
has the least decimal
places, so the result will
end with 4 decimal places,
0.0509.
http://www.astro.washington.edu/courses/labs/clearinghouse/lab
s/Scimeth/images/subtract.gif
1.
Why are the first few digits called certain numbers?
2.
Why do we use significant figures?
3.
Round 4.2786 x 10^3 to the nearest tens.
Solve (2.87 x 10^-2)(8.79x10^3) with the correct
number of sig figs
5. Explain the limiting term for adding and subtracting.
4.
 Answer 1: The first digits are always the same




regardless of who makes the measurement
Answer 2: Significant figures allow us to signify the
degree of certainty for a measurement
Answer 3: 4278.6  4279
Answer 4: (0.0287)(8970) = 252.273  252
Answer 5: The limiting term is the smallest number
with the least digits past the decimal.
 http://cyberbridge.mcb.harvard.edu/images/math2_1.png
 http://cyberbridge.mcb.harvard.edu/images/math2_2.png
 http://online.redwoods.cc.ca.us/instruct/milo/1/sld042.jpg
 http://www.astro.washington.edu/courses/labs/clearinghouse/labs/Scimeth/image
s/multiply.gif
 http://www.astro.washington.edu/courses/labs/clearinghouse/labs/Scimeth/image
s/division.gif
 http://www.astro.washington.edu/courses/labs/clearinghouse/labs/Scimeth/image
s/addition.gif
 http://www.astro.washington.edu/courses/labs/clearinghouse/labs/Scimeth/image
s/subtract.gif