1. Measurement In Science:
Certainty in Measurement:
Accuracy, Precision and Significant Figures
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2. Certainty in measurement
When measuring quantitative properties of matter you must use a measuring instrument.
Measuring instruments are generally graduated- made with marks to show levels of amounts
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3. Certainty in measurement
Some measuring instruments are more exact than others.
This means that every instrument has a certain level of uncertainty- inexactness
It is important to be clear about how exact and reliable a measurement is, so that you can decide whether it is trustworthy or not
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4. ACCURACY vs. PRECISION
Accuracy indicates how close a measurement is to the real amount.
Precision indicates how close together or how repeatable the results are.
A precise measuring instrument will give very nearly the same result each time it is used. ( Of course the repeated measurement, may or may not be accurate!)

5. QUESTION 1: HORSESHOES & HAND GRENADES
Watch 3 balls drop and say good or bad for precision and accuracy
PRECISION ?
GOOD! (HIGH)
REASON: All 3 of the results are close to each other
Target
ACCURACY?
POOR! (LOW)
REASON: All 3 results are WAY off the “actual” targeted value

6. HORSESHOES & HAND GRENADES
QUESTION 2:
Watch 3 balls drop and say good or bad for precision and accuracy
PRECISION ?
POOR! (LOW)
REASON: All 3 results are nowhere close to one another
ACCURACY?
POOR! (LOW)
REASON: All 3 results come nowhere near the “actual” targeted amount

7. HORSESHOES & HAND GRENADES
QUESTION 3:
Watch 3 balls drop and say good or bad for precision and accuracy
PRECISION ?
GREAT! (High)
REASON: All 3 results are right next to each other ( little difference)
ACCURACY?
GREAT! (High)
REASON: All 3 results are RIGHT ON the targeted “actual” amount

8. HORSESHOES & HAND GRENADES
QUESTION 4:
Watch 3 balls drop and say good or bad for precision and accuracy
PRECISION ?
PRETTY GOOD! (High)
REASON: All 3 are FAIRLY CLOSE to each other (not much difference)
ACCURACY?
PRETTY GOOD! (High)
REASON: All 3 are FAIRLY CLOSE to the targeted “actual” amount. (not much difference)

9. EXAMPLE :ACCURACY
Accurate Innacurate
100g
100g
98.89g
100.00g
Example: We'd expect a balance to read 100 grams if we placed a standard 100 g weight on the balance. If it does not, then the balance is inaccurate. (It does not come close to the “actual mass”)

10. EXAMPLE : PRECISION
More Precise
Less Precise
Trial #
Mass (g) 1
100.00 2
100.01 3
99.99 4
Average
Range
± 0.01
Std. Dev.
0.05
Trial #
Mass (g) 1
100.10 2
100.00 3
99.88 4
100.02
Average
Range
± 0.11
Std. Dev.
0.09
Example: Notice that the 4 measurements on the right are not as close to each other as the 4 readings on the right. They have less Precision

11. Reporting Measurements
Report what is known with certainty
Add ONE digit of uncertainty (estimation)
By adding additional numbers to a measurement – you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement.
Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

12. Measuring a Pin
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 122

13. Practice Measuring cm 1 2 3 4 5 4.5 cm cm 1 2 3 4 5 4.54 cm cm 1 2 3 41 2 3 4 5
4.5 cm
PRACTICE MEASURING
Estimate one digit of uncertainty.
a) 4.5 cm
b) * 4.55 cm
c) 3.0 cm
*4.550 cm is INCORRECT while cm or 4.58 cm are CORRECT (although the estimate is poor)
By adding additional numbers to a measurement – you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement.
In applying the rules for significant figures, many students lose sight of the fact that the concept of significant figures comes from estimations in measurement. The last digit in a measurement is an estimation.
How could the measurement be affected by the use of several different rulers to measure the red wire?
(Different rulers could yield different readings depending on their precision.)
Why is it important to use the same measuring instrument throughout an experiment?
(Using the same instrument reduces the discrepancies due to manufacturing defects.) cm 1 2 3 4 5
4.54 cm cm 1 2 3 4 5
3.0 cm
Timberlake, Chemistry 7th Edition, page 7

14. Implied Range of Uncertainty5 6 4 3
Implied range of uncertainty in a measurement reported as 5 cm.
When the plus-or-minus notation is not used to describe the uncertainty in a measurement, a scientist assumes that the measurement has an implied range, as illustrated above.
The part of each scale between the arrows shows the range for each reported measurement. 5 6 4 3
Implied range of uncertainty in a measurement reported as 5.0 cm. 5 6 4 3
Implied range of uncertainty in a measurement reported as 5.00 cm.
Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32

15. 20 ?
15 mL ?
1.50 x 101 mL
15.0 mL
A student reads a graduated cylinder that is marked at mL, as shown in the illustration.
Is this correct? NO
Express the correct reading using scientific notation mL or 1.50 x101 mL 10

16. How to Read a Thermometer (Celcius)10 10
100 5 5 5 50
4.0 oC
8.3 oC
64 oC
3.5 oC

17. Record the Temperature (Celcius)
60oC
6oC
50oC
5oC
25oC
100oC
100oC
40oC
4oC
20oC
80oC
80oC
30oC
3oC
15oC
60oC
60oC
20oC
2oC
10oC
40oC
40oC
10oC
1oC
5oC
20oC
20oC
0oC
0oC
0oC
0oC
0oC A
30.0oC
48oC
60.oC B
3.00oC C
19.0oC D E

18. Accuracy vs. Precision ACCURATE = Correct PRECISE = Consistent
Accuracy - how close a measurement is to the accepted value
Precision - how close a series of measurements are to each other
ACCURATE = Correct
PRECISE = Consistent
Courtesy Christy Johannesson

19. Accuracy vs. Precision Systematic errors: reduce accuracy
Scientists repeat experiments many times to increase their accuracy.
Good accuracy
Good precision
Poor accuracy
Good precision
Poor accuracy
Poor precision
Systematic errors:
reduce accuracy
Random errors:
reduce precision
(instrument)
(person)

20. Precision Accuracy check by check by using a repeating
                                                                                                                                                      
Precision
Accuracy
reproducibility
check by
repeating
measurements
poor precision
results from poor
technique
correctness
check by using a
different method
poor accuracy
results from
procedural or
equipment flaws.
nt/slides/sld016.htm

21. Types of errors Systematic Random Instrument not ‘zeroed’ properly
Reagents made at wrong concentration
Random
Temperature in room varies ‘wildly’
Person running test is not properly trained