ACCURACY
A description of how close measurement is to the
true or accepted value of a measurement.
Error or Absolute Error =
Observed value – accepted value
E = O-A
Error or Absolute Error =
Observed value – accepted value
E = O-A
• E = 10.2 cm – 10.5 cm
E = -0.3 cm
• E = 10.8cm – 10.5 cm
E = 0.3 cm
% ERROR =
observed value – accepted value X 100%
accepted value
% E = O – A x 100%
A
% E can have + or – value
What does negative value mean?
PRECISION
• The exactness of a measurement.
• How closely several measurements of the
same quantity made in the same way agree
with one another.
PRECISION (Uncertainty)
1. Determine average of values
2. Subtract the average from each measured
value. (deviation)
3. Add the absolute values of the deviations.
(sum of deviations from average)
4. Average of the sum = uncertainty
5. Report result as Average + uncertainty
25.0 + 0.001 cm 25.0 + 0.1cm
ACCURACY AND PRECISION
Significant Figures = digits of measured value known with
certainty and one estimated (doubtful)
Significant Figures
• What numbers are considered significant?
– All non-zero numbers are significant.
– Zeroes between significant digits are significant
– If there is no decimal point, then trailing zeroes
are not significant
– If there is a decimal point, then all trailing
zeroes are significant
– If a number is less than one, then the first
significant figure is the first non-zero digit after
the decimal point
Why are Sig Figs so Important?
• We have to interpret measured values made
by others
• A way to communicate accuracy and precision
of data without discussion
Trick to Remember
Operations with Sig Figs
• Addition/Subtraction
• Multiplication/Division
– Worksheet on operations
Practice
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1) 6.078 g + 0.3329 g =
2) 8.2 cm - 7.11 cm =
3) 0.8102 m x 3.44 m =
4) 94.20 g ÷ 3.167 22 ml =
5) 1.36 x 10 -5 x 5.02 x 10 -2 =
6) How many grams are in 882 g ?