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Significant Figures
Who cares?
Sig Figs measure the degree of precision of a
measurement.
But first: What’s the difference between accuracy and precision?
Do they mean the same thing?
Important definitions:
• accuracy: a measure of how closely a measurement agrees with the correct or true value
• precision: a measure of how closely individual measurements agree with one another
Example question:Two students measured the mass of a small pebble,
which had an actual mass of 2.35 grams.
Sally’s measurements were 2.78 grams, 2.82 grams, and 2.81 grams.
Madison’s measurements were 2.30 grams, 2.34 grams, and 2.41 grams.
Which student was more accurate?Which student was more precise?
A correctly precise measurement includes all
digitsthat are knownfor sure, plus a
digit that isestimated.
For example:
Another example:
Rules for counting sig figs:
There are ONLY two rules to remember when counting
the # of Sig Figs.
Rule #1: Don’t start counting till you get to a number that isn’t a zero.
Rule #2: Once you start counting, don’t stop till you’ve counted all the
digits, including zeroes.
And you need to remember a little geography:
Where is the Atlantic Ocean, and where is the Pacific Ocean?
How many sig figs are in this number: 273.5200?
Ask yourself:
Is the decimal point present or absent?
Answer: PresentCount from first non-zero
number starting at the Pacific side.
273.5200
Once you start counting, you don’t stop!
Examples2.55 3 S.F.0.2500 4 S.F.100.25 5 S.F.
Examples12.500.00500.0003
The first step is always to ask yourself:
Is the decimal point present or absent?
18,000,000
Answer: AbsentCount from first non-zero number
moving from the Atlantic side.
18,000,000
Examples135 3 S.F.100 1 S.F.10500 3 S.F.
Examples
350 0.0020
17,500 27.02
135.0 2060
Using sig figs in
calculations
Formultiplication
and division:
Your answer can not be more
precise than the least precise
measurement.
Think of Sloppy Joe
You and your lab partner, Sloppy Joe, have been assigned to find the area of your lab table. You carefully measure the length, and find it to be 233.65 cm. Sloppy Joe casually slides the meter stick along the width, suggests that it measures about 200 cm.
233.65 x 200 = 46730
5 S.F. 1 S.F. 4 S.F.?
Answer must be recorded as 50,000 cm2
It can have only one sig fig.
Your answer MUST
have the same number
of sig figs as the factor with the least
number of sig figs.
610 x 6.20 = 3782
2 S.F. 3 S.F.What is the correct answer?
3800
Example: You calculate the density of an object with mass of
24.300 grams, and volume of 62.5 ml. How many sig figs in
your answer? D=M/V
24.300/62.5 = 0.3888Correct Sig. Figs. = 0.389
Foraddition and
subtraction
Your answer can not contain more decimal places than the least
precise measurement.
Line up the decimal points in
the numbers.2.515 + 1.3 +12.00
=????
2.5151.3
+ 12.0015.815
Answer stops here
Scientific notation
The number of sig figs comes from the number written before the times sign.
Examples3.50 x 1023 3 S.F.
5.0 x 10 -4 2 S.F.
3 x 10-4 1 S.F.