1. Using Scientific Measurements
Chapter 2 section 3

2. Objectives 1. Distinguish between accuracy and precision.
2. Determine the number of significant figures in measurements.
3. Perform mathematical operations involving significant figures.
4. Convert measurements into scientific notation.

3. Accuracy and Precision
Accuracy is the closeness of a measurement to the correct (accepted) value of quantity measured.
Precision is a measure of how close a set of measurements are to one another.
To evaluate the accuracy of a measurement, the measured value must be compared to the correct value.
To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements

4. Accuracy vs Precision

5. Example: Accuracy
Who is more accurate when measuring a book that has a true length of 17.0 cm?
Susan:
17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm
Amy:
15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

6. Example: Precision
Who is more precise when measuring the same 17.0 cm book?
Susan:
17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm
Amy:
15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

7. Is it Accurate, Precise, Both or Neither?
Known Density = 3.11 g/mL
Test Results 3.77, 3.81, 3.76, 3.80
Precise, not accurate
Test Results 3.01, 3.89, 3.50, 5.99
Neither
Test Results 3.04, 3.20, 3.13, 3.07
Accurate, not precise
Test Results 3.11, 3.12, 3.12, 3.10
Both

8. What are some reasons for accuracy or precision being off?
Some error or uncertainty always exists in any measurement.
skill of the measurer
conditions of measurement
measuring instruments

9. What are some reasons for accuracy or precision being off?
Some rulers have more marks than others
Which ruler is more accurate?
Which ruler has more uncertainty?

10. How do we represent error?
Error is the difference between the actual (or accepted) value and the experimental value
Percent Error
Percent Error = Experimental – Accepted x100
Accepted

11. Accuracy - Calculating % Error
If a student measured the room width at 8.46 m and the accepted value was 9.45 m what was their accuracy?
Using the formula: % error = (Experimental - Accepted)÷ Accepted x100

12. Accuracy - Calculating % Error
Since Exp V = 8.46 m, AV = 9.45 m
% Error = (8.46 m – 9.45 m) ÷ 9.45 m x 100
= [ m ÷ 9.45 m ] x 100
= x 100
%Error = %
Note that the meter unit cancels during the division & the unit is %. The (-) shows that Exp V was low
The student was off by almost 11% & must remeasure
Acceptable % error is within 5%

13. Acceptable error is +/- 5%
Values from –5% up to 5% are acceptable
Values less than –5% or greater than 5% must be remeasured
remeasure -5%
5% remeasure

14. What is the student's percent error?
Example Problem #1
What is the student's percent error?
Working in the laboratory, a student finds the density of a piece of pure aluminum to be 2.85 g/cm3.  The accepted value for the density of aluminum is g/cm3.

15. A student takes an object with an accepted mass of 200
A student takes an object with an accepted mass of grams and masses it on his own balance.  He records the mass of the object as g.  
What is his percent error?
Example Problem #2

16. How to Check a Measurement for Precision
Significant Figures
How to Check a Measurement for Precision

17. Significant Digits & Precision
The precision of a measurement is the smallest possible unit that could be measured.
Significant Figures (sf) are the numbers that result from a measurement.
When a measurement is converted we need to make sure we know which digits are significant and keep them in our conversion
All digits that are measured are significant

18. Significant Digits & Precision
What is the length of the bar?
How many digits are there in the measurement?
All of these digits are significant
There are 3 sF cm 1 2 3 4
Length of Bar = 3.23 cm

19. Significant Digits & Precision
If we converted to that measurement of 3.23 cm to mm what would we get?
Right! mm
How many digits in our converted number?
Are they all significant digits (measured)?
Which ones were measured, and which ones were added because we converted?
If we know the significant digits, we can know the precision of our original measurement

20. Significant Figures & Precision
What if we didn’t know the original measurement – such as hm. How would we know the precision of our measurement.

21. Counting Significant Figures
Numbers 1-9 always count has 5 sig figs
Zeroes in front never count has 4 sig figs
Zeroes after decimal point AND a # count.
has 3 sig figs has 3 sig figs
Zeros between sig digits count has 3 sig fig has 4 sig fig

22. How many sig figs in: 3 2 4 1 5
5.05
1200
0.0005 50
50.00
123.45
8090

23. 2.3 Rounding Rules for rounding numbers: < 5, don’t round up.
Don't change the magnitude of the number.
what is magnitude?
How big or small the number is. Like is it in the thousands? Hundreds? Tenths? Billions? If a number is in the thousands, when you round it must STILL be in the thousands.

24. Round these numbers off to 3 significant figures.
1.84
$7160 NOT Seven thousand dollars is not the same as seven hundred dollars!!! (Magnitude)
24,900 1)
2) $ 3)
4) 24,925

25. 2.3 Adding and Subtracting
Addition and subtraction: Your final answer must have the same decimal places as the fewest decimal places. (Your answer can only be as accurate as the weakest link)
 Final answer = 2.35
Rounded to 2.35 since has two decimal places
Focus on Decimal Places

26. 2.3 Multiplication and Division
Your final answer has the same # sig dig as the LEAST sig dig.
3.546 x 1.4 =
= sig fig cause 1.4 is 2 sig fig
Focus on Sig Fig