Transcript n-C1-SigFigsPPT

Notes on
Significant Figures
(“Sig Figs”)
Mathematical tool used by scientists
when expressing measured data and
calculations involving measured data
Why am I just now finding out
about this?
• Sig figs are important “tools” used by ALL scientists, but
are generally not emphasized below Chemistry on the
high school level (why trouble their heads and Bio is not
as quantitative as Chemistry or Physics)
• Chemistry and Physics (the “Physical Sciences”) involve
many measurements – among them time, displacement,
velocity, moles, grams, liters, molarities, voltage,
frequency, radius, watts, etc!!!
• Chemists and Physicists therefore must present data in
a manner that all scientists will be able to:
– A) Trust the data
– B) Understand the level of sophistication of the equipment that
was used to take the measurments
Do Math Teachers use this system?
• Generally speaking, NO. The reason for that is
simple…
• Scientists use MEASURED VALUES (taken from
some instrument) and most math problems
involve “counted” numbers. (ie: How many
students are in the room? Not: How tall is that
student?)
• How tall must have a unit associated with it!
• Sig Figs help communicate the level of
sophistication of the measurement device
•THAT’S WHAT
SIG FIGS
DO!!!
Example
• Let’s say Ron takes a piece of yarn and
ties a knot the length of the yarn each
meter for 10 meters.
• Let’s say Jill has a meter stick.
• They both have to measure the length of
the lab counters in the classroom.
• Each one MUST have a different answer –
Ron’s will be less “precise” but each will
be “correct” if they “follow the rules”.
What is this measurement?
I’m measuring the same thing.
Shouldn’t the recorded value be the
same?
Rule 1 –
All non-zero digits are significant
Measurement
Number of Sig Figs
0.456m
3
1200g
2
95.7cm
3
0.88117m
5
Rule 2 –
Zeros between two non-zero digits are
significant (the “sandwich” rule)
Measurement
Number of Sig Figs
0.405g
3
9001m
4
20.03ml
4
10.8007kg
6
Rule 3 –
Zeros to the right of a decimal are significant if
they are also to the right of a non-zero digit
Measurement
Number of Sig Figs
4.00m
3
79.0030g
6
0.007cm
65000L
1
2
Let’s Explore that rule:
• Look at the difference in meaning
between:
• 4 miles – this person might be using a
map with a ruler that has a 10 mile scale
• 4.0 miles – this person might be reading a
map with a ruler that has a 1 mile scale
• 4.00 miles – this person might be reading
a map with a ruler that has a 0.1 mile
scale
Rule 4 –
Lone zeros are never significant
Measurement
Number of Sig Figs
0.456m
3
0.15g
2
0.230cm
3
0.88117m
5
Rule 5 –
Zeros to the left of an understood decimal are
not significant unless a line is used (or a
decimal is properly placed )
Measurement
Number of Sig Figs
40m
1
40.m
2
40.0m
3
93,000,000
2
How is a line used?
Measurement
Number of Sig Figs
1
2
3
4
Let’s Get Some Practice First:
• 35.1 kg
3
• 45,000 cm
• 80.2 mg
• 0.003 mm
2
3
1
0.40 m
200.0 L
2
4
2.500 km
4.50 x 103 g
4
3
Going Further…
• Well, at this point, any time a person on the
street asks you how many sig figs there are
in a number, now you’ll know.
• Seriously, though…none of this is important
unless you are taking empirical data.
• Empirical data describes the simplest type of
data – such as the length of an index card in
cm or the mass of a kidney bean in grams,
• As chemists and physicists, this is what
we’re all about!
Using Sig Figs in Calculations
• Just stating that a pane of glass measures
9.92 cm on a side communicates
something about the device used to
measure that length.
• However, often times we need to know the
area covered or the volume of the object.
• Most often, your labs will involve
calculating some values. There are some
simple rules for manipulating this data.
Rule for Multiplying and Dividing
with Significant Figures
• The final answer must have no more sig
figs than the measurement with the least
number of sig figs
• Let’s say all measurements are in cm:
890
• 42.4 x 21 = 890.4 (calculator)
• 100 x 24.887 = 2488.7 (calculator) 2000
• 29.9 x 0.005 = 0.1495 (calculator) 0.1
• 87.9 / 0.40 = 2197.5 (calculator) 2200
• 35.000 / 7.00 = 5 (calculator) 5.00
Rule for Adding and Subtracting
with Significant Figures
• The final answer must have no more
decimal places than the measurement with
the least number of decimal places
• Let’s say all measurements are in cm:
63
• 42.4 + 21 = 63.4 (calculator)
• 0.10 + 24.887 = 24.987 (calculator) 24.99
• 30.0 - 0.005 = 29.995 (calculator) 30.0
88.30
• 87.90 + 0.40 = 88.3 (calculator)
• 35.000 - 7.00 = 28 (calculator) 28.00