Transcript Accuracy, significant figures, and scientific notation powerpoint

Do Now
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Take a copy of the worksheet
Organizing Data from the front
desk.
Bring it back to your seat and work
on it for the first 10 min. of class.
Accuracy vs. Precision
Accuracy --
the extent to which a reported
measurement approaches the
true value of the quantity measured.
Precision--
the degree of exactness of a
measurement.
Accuracy and Precision
Scientific Notation
When numbers are very large or very
small it can be very cumbersome to write
all those zeros.
For example the mass of the earth is
about
5,970,000,000,000,000,000,000,000 kg
scientists prefer to write it this way
5.97 x 1024 kg
Scientific Notation
Scientific notation works by dividing out
the appropriate factor of 10.
104 =10,000
103 =1,000
102 =100
101 =10
100 =1
10-1 =0.1
10-2 =0.01
10-3 =0.001
10-4 =0.0001
Scientific Notation
7,359,845. m = 7.359845 x 106 m
45.6 kg = 4.56 x 101 kg
0.002389 s = 2.389 x 10-3 s
Significant Figures
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Significant figures are the digits in a
measurement that are known with
certainty.
How precise of a measurement can we make with a ruler like this one?
Significant Figures
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Significant figures are the digits in a
measurement that are known with
certainty.
How precisely can we measure mass with a triple beam balance like this one?
Significant Figures
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Significant figures are the digits in a
measurement that are known with
certainty.
Which instrument will give me a more precise volume measurement?
Measure your lab bench.
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Go to a bench with your lab group.
Have each member measure the length of
the bench with a meter stick and with a video
cassette.
Record all the data in a table.
Significant Figure Rules
1.All nonzero digits are significant:
1.243 g has 4 significant figures,
1.2 g has 2 significant figures.
Significant Figure Rules
1.All nonzero digits are significant:
2.Zeros between nonzero digits are significant:
Significant Figure Rules
1.All nonzero digits are significant:
2.Zeros between nonzero digits are significant:
1002 kg has 4 significant figures,
3.07 mL has 3 significant figures.
Significant Figure Rules
1.All nonzero digits are significant:
2.Zeros between nonzero digits are significant:
3.Leading zeros to the left of the first nonzero digits
are not significant; such zeroes merely indicate
the position of the decimal point:
0.001 mL has only 1 significant figure,
0.012 g has 2 significant figures.
Significant Figure Rules
1.All nonzero digits are significant:
2.Zeros between nonzero digits are significant:
3.Leading zeros to the left of the first nonzero digits
are not significant; such zeroes merely indicate
the position of the decimal point:
4.Trailing zeros that are also to the right of a decimal
point in a number are significant:
5.When a number ends in zeros that are not to the
right of a decimal point, the zeroes are not
necessarily significant:
190 miles may be 2 or 3 significant figures,
50,600 calories may be 3, 4, or 5 significant
figures
Significant Figure Rules
The potential ambiguity in the last rule can be avoided
by the use of scientific notation. For example,
depending on whether the number of significant
figures is 3, 4, or 5, we would write 50,600
calories as:
5.06 x 104 calories (3 significant figures),
5.060 x 104 calories (4 significant figures), or
5.0600 x 104 calories (5 significant figures).
Significant Figures
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8.753469 cm
3 cm
When multiplying
measurements, the
answer is only as
precise as the
LEAST precise
measurement.
Area = length × width
= 8.753469 × 3 = 26.260407
However our least precise number
is 3 which has one significant figure
Therefore
2
Area = 30cm
Wrap Up
Homework:
Complete the worksheet Study Guide:
Section 1.3 and bring it in for next class.