precision, accuracy and significant figures notes
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Precision, Accuracy and Significant Figures Notes
Today’s Objectives
Compare and contrast accuracy and precision.
Identify the purpose of significant figures. Multiply, divide and add and subtract using
significant figure rules.
Precision vs. Accuracy
Accuracy
Accuracy is how close something comes to an accepted standard.
Precision
Precision - how fine the divisions or segments are and how repeatable the results.
Accurate = Correct
Precision = Consistent
Ideally an instrument is both accurate and precise
Precision can add to accuracy if the instrument is calibrated correctly.Deduct if not
Example: Tare (zero) a scale
Significant Figures Purpose
Significant digits carry the precision of the instrument used.
Why do them?Consistency between peopleEnsures that the precision of the results only
reflect the precision of the least precise measuring tool
If a sprinter is measured to have completed a 100.0 m race in 11.71 seconds, what is his average speed?
Average speed = 8.53970965 m/s Can we really measure a sprinter’s speed
that precisely?
Other Options Include:
8.53970965 m/s 8.5397097 m/s 8.539710 m/s or
8.53971 (What is the difference?)
8.53971 m/s
8.5397 m/s 8.540 m/s or 8.54 m/s
(What is the difference?)
8.54 m/s 8.5 m/s 9 m/s Which would you
choose?
Candle with a mass of 14.143g 2.7 hours is the burn time.
14.143g/2.7 hrs = 5.238148148 g/hr
This number magically became more precise
One who makes a square’s side 5.1 cm x 5.1 cm is not confident that the square is exactly 26.013496870584764240556 cm2.
Nor would it be useful to say the square is 30 cm2
One has to be careful claiming a greater precision than what is justified
A good rule of thumbNo final answer should have any
more precision attached to it than the LOWEST precision found among the numbers being worked.
Another words… you answer should not have more digits than the original numbers calculated
Significant Figures Practice
Sig Fig – Rules
Nonzero numbers are always significant
1.2343876493
Sig Fig – Rules
All final zeros after the decimal point are significant
1.000000, 345.600
Sig Fig – Rules
Zeros between two other significant digits are always significant.
1.001, 234.01, 3.404040
Sig Fig – Rules
Zeros used solely as placeholders are not significant.
0.0002, 0.0231, 0.003040
Practice Time
How Many Sig Figs?
10010.980.00340.0480
How Many Sig Figs?
6.04903030004.030.00000010
Calculating With Sig Figs
Scientific Notation shows you how many sig. figs are in the number.
Ex.2.5x102 This is 2 sig. figs.
1.0000x10-23 This has 5 sig. figs.
Calculating With Sig Figs
Adding and Subtracting Sig. Figs.
RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.Example: When we add
3.76 g + 14.83 g + 2.1 g = 20.69 g 20.7g
Calculating With Sig Figs Multiplying and Dividing with Sig. Figs.
RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits.Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm3We look to the original problem and check the number of significant digits in each of the original measurements: Our answer can only show 3 significant digits because that is the least number of significant digits in the original problem.5946.50525 shows 9 significant digits, we must round to the tens place in order to show only 3 significant digits. Our final answer becomes 5950 cm3.
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