1. Reliability of Measurements

2. Measurements
Much of what we know about the physical world has been obtained from measurements made in the lab
Quantitative Observations
three parts to any measurement
Numerical value
Unit of measurement
An estimate of uncertainty

3. Uncertainty All Measurements have some degree of error User error
Instrument Error
Description of Error
Accuracy and Precision

4. Accuracy
Correct
A measurement is accurate if it correctly reflects the size of the thing being measured

5. Precision
"repeatable, reliable, getting the same measurement each time.“
Determined by the scale on the instrument

6. Precise and Accurate
This pattern is both precise and accurate. The darts are tightly clustered and their average position is the center of the bull's

7. Neither Accurate nor Precise
This is a random-like pattern, neither precise nor accurate. The darts are not clustered together and are not near the bull's eye.

8. What Effects Accuracy & Precision
PRECISION: – is a determination of the reproducibility of a measurement.
– tells you how closely several measurements agree with one another.
– precision is affected by random errors.
ACCURACY: – closeness of a measurement to a true, accepted value.
– is subject to systematic errors (errors which are off in the same direction, either too high or too low)
What went wrong?
· The balance may not have been zeroed,
· The pan of the balance may have been dirty?
The instrument is damaged
The skills of the user are bad

9. Measurements and Significant Figures
Numerical value must be recorded with the proper number of significant figures.
The number of significant figures depends on the scale of the instrument used and is equal to the known from the marked scale plus on estimated digit.
This last digit gives the uncertainty of the measurement and gives the precision of the instrument.
Scientist indicate the precision of a measurement with the use of significant figures
A system to communicate the precision of measurements
Agreed Upon by all
All known digits plus one estimated digit

10. The Metric Ruler Marked to the ones Estimate to the tenths place
Less precise
9.5 cm
Marked to the tenths
Estimate to the hundredths place
More precise
9.51 cm

11. Calculations of Error Error = (measured value – accepted value)
Percent Error = (measured value – accepted value) ÷ accepted value x 100 %

13. Two kinds of numbers in science
Two kinds of numbers are used in science:
· Exact or Defined:
exact numbers; no uncertainty
· Measured
are subject to error; have uncertainty

14. Comparing Measurements
Decigram
Balance
Centigram
Milligram
Analytical
Mass Reading
3.1 g
3.12 g
3.121 g g
Sig. Figs 2 3 4 5
Less precise
More precise
Even more precise
Most precise

15. Rules for Recognizing Significant Figures
Non-Zero digits are significant.
256
36999 45
Any zeroes between two sig figs are significant.
205
1.0002
Final zeroes to the right of the decimal point are significant.
1.0
78.200
Placeholder zeroes are not significant. Convert to scientific notation to remove these placeholder zeroes.
2000
.01
.010
1.5 x 10
x 10
8.90 x 10
Counting numbers and defined constants have an infinite number of sig figs.

16. Significant Figures in Calculations
The answer to a calculation with measurements can be no more precise than the least precise number.

17. Addition and Subtraction
When you add and subtract with measurements your answer must have the same number of digits to the right of the decimal point as the value with the fewest digits to the right of the decimal point.
 Example
28.00 cm cm cm = cm rounded to 2 places past the decimal cm

18. Multiplication and Division
When you multiply and divide with measurements your answer must have the same number of significant digits as the measurement with the fewest significant figures.
Example
Calculate the volume of the rectangle that is cm long, 3.20 cm high, and 2.05 cm wide.
V = l x w x h
V = 3.20cm x 2.05 cm x 3.65 cm = cm rounded to 3 sig figs = 23.9 cm3

19. Rounding If the rounded digit is < 5, the digit is dropped
If the rounded digit is > 5, the digit is increased
Example 1
g rounded to 3 sig figs 7.78 g
124 g rounded to 2 sig figs 120g
% rounded to 2 sig figs 14 %
g rounded to 2 sig figs g

20. Example 2
When performing multi step calculations, it is often better to carry the extra digits and round in the final step.
Calculate the volume of a cylinder with a diameter of 1.27 cm and a height of 6.14 cm
V = ∏d2h 4
V = cm3 round to 3 sig figs = cm3