Download Sig Figs/Scientific Notation - Ms. Simmons

Significant Figures and
Scientific Notation
What is a Significant Figure?
There are 2 kinds of numbers:
Exact: the amount of money in
your account. Known with
certainty.
Approximate: weight, height—
anything MEASURED. No
measurement is perfect.
What is a Significant Figure?
The numbers reported in a
measurement are limited by the
measuring tool
Significant figures in a
measurement include the known
digits plus one estimated digit
Using Significant Figures
When a measurement is
recorded only those digits that
are dependable are written
down.
The numbers reported in a
measurement are limited by the
measuring tool
Rules for Significant Figures
1. All non-zero digits in a number
are significant
2. Zeros between nonzero numbers
are significant
41,026
32.001
Count these
Learning Check
How many Significant Figures?
7.16
25
1.9648
43.104
2.0003
Rules for Significant Figures
3. Trailing zeros are not significant
8100
3,600,000
4. All numbers after a decimal
point are significant except for
leading zeros
0.365
0.00972
Do not count these
Learning Check
How many Significant Figures?
34,500
28.077
1,600
0.039
34,500.0
Sig Figs in Scientific Notation
5. All numbers in scientific notation
are significant. When writing
scientific notation, do not write a
number that is not meant to be a
sig fig.
3.2 x 103
2.00 x 10-4
Learning Check
How many Significant Figures?
2.62 x 10-2
1.0 x 102
9.7000 x 108
5 x 104
3 x 10-6
Sig Figs in Calculations
A calculated answer cannot be more
precise than the measuring tool.
A calculated answer must match the
least precise measurement.
Significant figures apply to final answers
from
1) adding or subtracting
2) multiplying or dividing
11
Adding and Subtracting
The answer has the same number of
decimal places as the measurement
with the fewest decimal places.
25.2
one decimal place
+ 1.34 two decimal places
26.54
answer 26.5 one decimal place
Learning Check
What is the answer to this calculation
with the correct number of sig figs?
16.309
230.4
+
1.6975
248.4065
248.4
Do not count/record these
Multiplying and Dividing
The answer has the same number of sig
figs as the least precise measurement.
Round the answer to this number.
4.15
3 sig figs
x 20
1 sig fig
83
must round to 1 sig fig 80
Learning Check
What is the answer to this calculation
with the correct number of sig figs?
2.54 x 0.0028
= 11.2888889
0.0105 x 0.060
Round to 2 sig figs
11
Do not count these
Precision vs. Accuracy
 Precision is a measurement of how much random
error exists in a measurement.
103.1008 is very precise
Relationship of
precision to
103 is less precise
significant figures.
100 is least precise
 Accuracy is a measurement of how much systematic
error exists in a measurement.
If an instrument is not calibrated correctly, it
may give an answer which is not accurate.
Precision vs. Accuracy
 Precision:
103.1
96.2
114.8
This set of data shows a lack of consistency. The margin
of error on the measurement is large. The data is not
very precise.
 Accuracy:
42.443 g 42.441 g
42.444 g
This set of data shows a high level of consistency, but
the mass being measured is known to be 45.000 g. The
balance is giving a systematic error – the reading is
consistently off by approximately 2.5 g. The balance may
give reliable comparisons of objects, but does not give a
reliable value for a single object.
Precision vs. Accuracy
 Precision refers to the closeness of two or more
measurements to each other. If you weigh a given
substance five times, and get 3.2 kg each time, then
your measurement is very precise.
 Accuracy refers to the closeness of a measured
value to a standard or known value. In lab you
obtain a weight measurement of 3.2 kg for a given
substance, but the actual or known weight is 10 kg.
Your measurement is not accurate.
Precision vs. Accuracy
Precision is independent of accuracy.
You can be precise but inaccurate: you measure
a mass to be almost identical four times, but the
measurement is not close to the known value.
You can be accurate but not precise: your
measurements are close to the known value,
but the measurements are far from each other.
Precision vs. Accuracy
precise and accurate
precise but not accurate
neither precise
nor accurate
accurate but not precise
Precision vs. Accuracy
A good analogy for understanding accuracy and
precision is to imagine a basketball player shooting
baskets. If the player shoots with accuracy, his aim
will take the ball close to or into the basket. If the
player shoots with precision, his aim will always
take the ball to the same location which may or may
not be close to the basket. A good player will be
both accurate and precise by shooting the ball the
same way each time and each time making it in the
basket.