1. How big is the beetle? Measure between the head and the tail!
Between 1.5 and 1.6 in
Measured length: 1.54 in
The 1 and 5 are known with certainty
The last digit (4) is estimated between the two nearest fine division marks.
Copyright © by Fred Senese

2. Chapter One: Measurement
1.4 Working with Measurements

3. 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.

4. 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?

5. 1.4 Working with Measurements
Digits that are always significant:
Non-zero digits.
Zeroes between two significant digits.
All final zeroes to the right of a decimal point.
Digits that are never significant:
Leading zeroes to the right of a decimal point. (0.002 cm has only one significant digit.)
Final zeroes in a number that does not have a decimal point.

6. Significant digits in mathematical operations
For multiplication or division, the number of significant digits in the result is the same as the number in the least precise measurement used in the calculation.
1.342 × 5.5 =  7.4

7. Significant digits in Mathematical Operations
For addition or subtraction, the result has the same number of decimal places as the least precise measurement used in the calculation.

8. What is area of 8.5 in. x 11.0 in. paper? Looking for: Given:
Solving Problems
What is area of 8.5 in. x 11.0 in. paper?
Looking for:
…area of the paper
Given:
… width = 8.5 in; length = 11.0 in
Relationship:
Area = W x L
Solution:
8.5 in x 11.0 in = 93.5 in2
# Sig. fig = 94 in2

9. 1.4 Working with Measurements
Using the bow and arrow analogy explain how it is possible to be precise but inaccurate with a stopwatch, ruler or other tool.

10. 1.4 Resolution
Resolution refers to the smallest interval that can be measured.
You can think of resolution as the “sharpness” of a measurement.

11. 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.

12. 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”.

13. 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

14. Is there a significant difference in data? Looking for: Given:
Solving Problems
Is there a significant difference in data?
Looking for:
Significant difference between two data sets
Given:
Table of data
Relationships:
Estimate error, Average error, 3X average error
Solution:
There is not a significance difference between and because:
= and 3x0.0002=0.0006
0.0003<