Transcript significant

Chapter One: Measurement
1.1 Measurements
1.2 Time and Distance
1.3 Converting Measurements
1.4 Working with Measurements
Section 1.4 Learning Goals
Determine the number of
significant figures in
measurements.
Distinguish accuracy, precision,
and resolution.
Compare data sets to determine
if they are significantly different.
Investigation 1C (Optional)
Significant Digits
Key Question:
How do we make precise measurements?
1.4 Working with Measurements
 In the real world it is
impossible for
everyone to arrive at
the exact same true
measurement as
everyone else.
Find the length of the
object in centimeters.
How many digits does your
answer have?
1.4 Working with Measurements
Digits that are always significant:
1. Non-zero digits.
2. Zeroes between two significant digits.
3. All final zeroes to the right of a decimal
point.
Digits that are never significant:
4. Leading zeroes to the right of a decimal
point. (0.002 cm has only one significant
digit.)
5. Final zeroes in a number that does not
have a decimal point.
Solving Problems
What is area of 8.5 in. x 11.0 in. paper?
1. Looking for:
 …area of the paper
2. Given:
 … width = 8.5 in; length = 11.0 in
3. Relationship:
 Area = W x L
4. Solution:
 8.5 in x 11.0 in = 93.5 in2
# Sig. fig = 94 in2
1.4 Working with Measurements
 Accuracy is how close a
measurement is to the accepted,
true value.
 Precision describes how close
together repeated
measurements or events are to
one another.
1.4 Working with Measurements
 Using the bow
and arrow
analogy explains
how it is possible
to be precise but
inaccurate with a
stopwatch, ruler
or other tool.
1.4 Resolution
 Resolution refers to the smallest
interval that can be measured.
 You can think of resolution as the
“sharpness” of a measurement.
1.4 Significant differences
 In everyday conversation, “same” means
two numbers that are the same exactly,
like 2.56 and 2.56.
 When comparing scientific results
“same” means “not significantly
different”.
 Significant differences are differences
that are MUCH larger than the estimated
error in the results.
1.4 Error and significance
 How can you tell if two results are the
same when both contain error
(uncertainty)?
 When we estimate error in a data set, we
will assume the average is the exact
value.
 If the difference in the averages is at
least three times larger than the
average error, we say the difference is
“significant”.
1.4 Error
 How you can you
tell if two results
are the same when
both contain error?
Calculate error
Average error
Compare average
error
Solving Problems
Is there a significant difference in data?
1. Looking for:
 Significant difference between two data sets
2. Given:
 Table of data
3. Relationships:
 Estimate error, Average error, 3X average error
4. Solution:
The difference between the averages: (2.6 – 2.1) = 0.5
0.5 is five times greater than the largest estimated error (0.1), so the
results are significantly different; the groups probably had different brands
of mints!