Transcript Accuracy and Precision notes

What is the difference between accuracy and precision?
= average position
Good precision
Low accuracy
Low precision
High accuracy
Significant figures: represent the precision of a measurement
A 20 g weight is weighed on four different balances, and the
four masses shown below were obtained. Which
measurement is the most precise?
# sig figs
19.9 g
19.94 g
19.935 g
19.9351 g
3
4
5
6
19.9351 g is the most precise. It has the greatest number of
significant figures.
Determining the number of significant figures:
1. All nonzero figures are significant.
2. The only time zeros are NOT significant is when they
precede nonzero numbers. They are merely placeholders.
Value
Sci. Notation
#SigFigs?
1.15
1.15
3
101.5
1.015 x 102
4
101.50
1.0150 x 102
5
0.015
1.5 x 10-2
2
0.00150
1.50 x 10-3
3
Math with significant figures:
Addition/subtraction: line up the decimal points. The answer is
rounded to the same number of decimal places as the value
with the least number of decimal places.
For example, add: 28.0 cm + 23.542 cm + 25.64 cm
Rounding Rules:
28.0 cm
23.542 cm
+ 25.64 cm
(77.182 cm)
77.2 cm
1. Round up if the next number is
greater than 5.
2. Round down if the next number is
less than 5.
3. If the next number is exactly 5, round
up only if the number to be rounded
is ODD.
Ex: 1.15 and 1.25 both round to 1.2
Math with significant figures:
Multiplication/division: the answer is rounded so that it
has the same number of sigfigs as the value with the
least number of sigfigs.
(3.205 cm)(3.65 cm)(2.05 cm) =
#sigfigs
4
3
3
(23.814 cm3)
23.8 cm3
What is the answer using the correct number of sigfigs to:
(2.005 g/mL)(2.05 mL + 1.6 mL)= 7.3 g
(2.005 g/mL)(3.65 mL) = 7.32 g
2 sf’s
2 sf’s
The six is underlined because it is the last significant digit.
Do not round off any values until the final answer!!
Accuracy of a measurement can be determined by calculating
the percent error (error = true – experimental).
error
x 100
Percent error =
true value
A 20.0000 g weight is weighed on four different balances,
and the four masses shown below were obtained. Calculate
the percent error for each measurement.
19.9 g
20.04 g
20.044 g
19.9351 g
error
0.1 g
0.04 g
0.044 g
0.0649 g
% error
0.5%
0.2%
0.22%
0.324%