Transcript Uncertainty and error in measurement

MEASUREMENTS
1
MEASUREMENT AND DATA PROCESSING 1

SIGNIFICANT DIGITS

PRECISION & ACCURACY

http://web.me.com/dbyrum/Ris/Resources/page29/files/ErrorAnalysis.pdf
http://www.wellesley.edu/Chemistry/Chem105manual/Appendices/uncertainty_analysis
.html
Imp:
 http://chemwiki.ucdavis.edu/Analytical_Chemistry/Quantifying_Nature/Uncertainties_in_
Measurements

TYPES OF OBSERVATIONS AND
MEASUREMENTS
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We make QUALITATIVE
observations of reactions —
changes in color and physical state.
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We also make QUANTITATIVE
MEASUREMENTS, which involve
numbers.
SIGNIFICANT DIGITS

http://chemsite.lsrhs.net/measurement/sig_fi
g.html
RULES
Rules for deciding the number of significant figures in a
measured quantity:
(1) All nonzero digits are significant:
1.234 g has 4 significant figures
(2) Zeroes between nonzero digits are significant:
1002 kg has 4 significant figures
(3) Leading zeros to the left of the first nonzero digits are not
significant; such zeroes merely indicate the position of the
decimal point: (placeholders are not significant)
0.012 g has 2 significant figures.
(4) Trailing zeroes that are also to the right of a decimal point
in a number are significant:
0.0230 mL has 3 significant figures,
0.20 g has 2 significant figures
(5) When a number ends in zeroes that are not to the right of a
decimal point, the zeroes are not necessarily significant:
190 miles may be 2 or 3 significant figures,
50,600 calories may be 3, 4, or 5 significant figures.
Trayling zeros:
 190000 = 2 s.d ( could be up to 6)
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In the last example, where the number 19000
has an ambiguous number of significant digits,
scientific notation will clear up this problem.
1.90 x 104= 19000 and has 3 significant digits.
 1.9 x 104= 19000 and has 2 significant digits.
 1.9000 x 104= 19000 and has 5 significant
digits.
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PROBLEMS:
1) 7000
 2) 450.0
 3) 350
 4) 0.006200
 7) 565.05
 8) 5500
 9) 74.00
 10) 7040.0
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IB PROBLEM:
RULES FOR MATHEMATICAL OPERATIONS:
In carrying out calculations, the general rule is that the
accuracy of a calculated result is limited by the least
accurate measurement involved in the calculation.
I.
In addition and subtraction, the result is rounded off so
that it has the same number of decimal places as the
measurement having the fewest decimal places.
For example,

100 (3 s.f) + 23.643 (5 s.f) = 123.643, which should be
rounded to 124 (3 s.f).
II. In multiplication and division, the result should be
rounded off so as to have the same number of
significant figures as in the component with the
least number of significant figures.
When there are series of calculations, do not round off until
the end.
For example,
3.0 (2 s.f ) × 12.60 (4 s.f) = 37.8000 which should be rounded off to 38 (2
s.f).
PROBLEMS:

http://www.fordhamprep.org/gcurran/sho/sho
/lessons/lesson23.htm
PRECISION AND ACCURACY IN
MEASUREMENTS
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Precision
How reproducible are
measurements?

Accuracy
How close are the
measurements to the
true value.
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PRECISION&ACCURACY
Accuracy
Accuracy, measures the agreement
between a measurement and
the accepted standard value.
Refers to how close a
measurement is to the real
value.
If a balance consistently gives a
value of 3.64 g on repeated
measurements, its precision is
good. However, if the actual
mass is 3.75 g, its accuracy is
poor!
Precision
Precision measures the agreement
between results of repeated
measurements.
Refers to reproducibility or how
close the measurements are to
each other.
A balance that can read mass to
0.0001 grams should be more
precise than one that reads
mass to 0.1 grams.
PRECISION OF A MEASUREMENT
Measurement ≈ 26.13 cm


The last digit is an
estimate.
The precision is limited
by the instrument.
Science, Measurement, Uncertainty and Error
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IB PROBLEM
The goal in the Chemistry laboratory is to obtain
reliable results while realizing that there are
 errors inherent in any laboratory technique.
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
http://www.savitapall.com/scientific_measuremen
t/notes/measurement%20and%20data%20proce
ssing.pdf

http://teachers.rickards.leon.k12.fl.us/Teacher
s/mcdonald/Senior%20IBAP%20Webpages/No
tes/11.%20Measurement%20and%20Data%2
0Processing/Measurement%20and%20IA.%20
DP,%20CE.htm
HTTP://WWW.DARTMOUTH.EDU/~CHEMLAB/INFO/RESOURCES/UNCERTAIN.HTML

http://www.wellesley.edu/Chemistry/Chem105
manual/Appendices/uncertainty_analysis.html