Accuracy and Precision
•Accuracy is the closeness of measurements to
the correct or accepted value of the quantity
measured.
•Precision is the closeness of a set of
measurements of the same quantity made in the
same way (close to one another, but not
necessarily close to accepted value.
•Percent error is calculated by subtracting the
accepted value from the experimental value,
dividing the difference by the accepted value,
and then multiplying by 100.
Experiment al value - Accepted value
x 100
Accepted value
Sample Problem:
A student measures the mass and volume of
a substance and calculates its density as
1.40 g/mL. The correct, or accepted, value of
the density is 1.30 g/mL. What is the percentage
error of the student’s measurement?
Experiment al value - Accepted value
x 100
Accepted value
% Error =
1.40 g/mL - 1.30 g/mL
1.30 g/mL
x 100 = 7.7%
Notice that the student’s percentage error is a positive number.
•(-) Percent Error – accepted value is greater
than experimental value
•(+) Percent Error – accepted value is less than
experimental value
In the sample problem the student’s experimental
value was 1.40 g/mL and the accepted value
was 1.30 g/mL. His percentage error was
positive.
•Error or uncertainty always exists in any
measurement. The skill of the measurer or
instrument may affect the outcome.
Significant Figures
•Significant Figures in a measurement consist
of all the digits known with certainty plus one
final digit, which is somewhat uncertain or is
estimated.
•The term “significant” does not mean certain.
What value should
be recorded for the
length of this nail?
What digit should be
recorded first?
Second?
Third?
6. 3 5 cm
Do we need to add a unit?
Rules for Determining Significant Zeros
1.Zeros appearing between nonzero digits
are significant.
Example: 1001 has 4 significant figures.
2.Zeros appearing in front of all nonzero
digits are not significant.
Example: 0.004 has 1 significant figure.
3.Zeros at the end of a number and to the
right of the decimal point are significant.
Example: 0.004500 has 4 significant figures.
4.Zeros at the end of a number but to the
left of a decimal point may or may not be
significant. If a zero has not been
measured or estimated but is just the
placeholder, it is not significant. A
decimal point placed after zeros indicated
that they are significant.
Example: 500 has 1 significant figure
500. has 3 significant figures
500.0 has 4 significant figures
Addition or Subtraction with
Significant Figures
•When adding or subtracting decimals, the
answer must have the same number of digits
to the right of the decimal point as there are
in the measurement having the fewest digits
to the right of the decimal point.
Example:
3 decimal
places
2.35 cm
+ 1.359 cm
3.709 cm
3.71 cm
2 decimal
places
answer can
only have 2
decimal places
Multiplication and Division with
Significant Figures
•For multiplication or division, the answer can
have no more significant figures than are in
the measurement with the fewest number of
significant figures.
Example:
2.35 cm x 4.1456 cm = 9.74216 cm2
9.74 cm2
3 significant
figures
5 significant
figures
Round to 3
significant figures