Transcript Accuracy & Precision

Significant Figures
And Mathematical Calculations
Significant Figures
At the conclusion of our time
together, you should be able to:
1. Determine the number of significant figures
needed for an answer involving calculations.
2. Round math problems properly
Rules for Rounding Off



If the digit to be removed
• is less than 5, the preceding digit stays
the same
• is equal to or greater than 5, the
preceding digit is increased by 1
In a series of calculations, carry the extra
digits to the final result and then round off
Don’t forget to add place-holding zeros if
necessary to keep value the same!!
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Significant Figure Math Rules
Addition / Subtraction Problem:
Example =
0.010 m using meter stick
0.0102 m using ruler
0.0102 m using calipers
0.010194 m using
micrometer
To find the total =
0.040594 m

But most of my measurements have fewer
decimal places than my best tool!!!
Significant Figure Math Rules

Addition / Subtraction:
Answers can’t have more numbers to the
right of the decimal point than the number in the
problem with the least amount of numbers to
the right of the decimal point.
Example =
Calculator says:
Answer:
24.1 m + 3.35 m + 2.23 m
29.68 m (wrong)
29.7 m
Adding and Subtracting
The answer has the same number of decimal
places as the measurement with the fewest
decimal places.
25.2 m
one decimal place
+ 1.34 m two decimal places
26.54 m
answer 26.5 m (one decimal place)
Significant Figure Math Rules

Multiplication / Division Problem:
14.1 cm
3.3 cm
4.23 cm2
42.3 cm2
46.53 cm2
What should my answer be??
Significant Figure Math Rules

Another Multiplication / Division
Problem: Find the volume?
0.041m high
0.091 m wide
0.034 m deep
0.0001269 m3
What should my answer be??
Significant Figure Math Rules

Multiplication / Division:
Your answer can’t have more sig figs than
the number in the problem with the least
amount of sig figs
Example = 60.56227892 cm x 35.25 cm
Calculator says: 2134.890832 cm2 (wrong)
Answer:
2135 cm2
Significant Figures and
Exact Numbers
60 seconds in 1
minute
25 cents in 1
quarter
Some numbers are
exact: There are
There is no uncertainty
in any of these numbers.
12 eggs in one
dozen
In other words there are
12.0000000000000000000000000000000000
eggs in 1 dozen
(add as many zeros as you like)
Sig. Figs. And Counting Numbers
 Counting
 Ex:
numbers have infinite sig figs.
3 apples
= 3.00000000…. apples
Chemical Compound Quiz
Which is denser: ice or water?
Water
Why??
Ice Expands 1/7th!!!
Significant Figures
Lets’ see if you can:
1. Determine the number of significant figures
needed for an answer involving calculations.
2. Round math problems properly
Learning Check
A. 2.19 m X 4.2 m =
1) 9 m2
2) 9.2 m2
B.
C.
4.311 m ÷ 0.07 m =
1) 61.58
2) 62
2.54 m X 0.0028 m =
0.0105 m X 0.060 m
1) 11.3
2) 11
3) 9.198 m2
3) 60
3) 10
Learning Check
In each calculation, round the answer to the
correct number of significant figures.
A. 235.05 m + 19.6 m + 2.1 m =
1) 256.75 m
2) 256.8 m
3) 257 m
B.
58.925 m - 18.2 m =
1) 40.725 m
2) 40.73 m
3) 40.7 m
Euphemisms in Science
We all know that some politicians and government
spokesmen use certain euphemistic phrases to give an
aura of respectability to descriptions of events or actions
which would be offensive when expressed in plain English.
The following is a list of Euphemisms in Science and their
translations into plain English.
“Handled with extreme care during the experiments...”
Not dropped on the floor!