Physics
REQUIRED SKILL
Recognizing
Accuracy and Precision
For many students, the distinction between precision and accuracy is NOT clear. A
measurement can be precise, accurate, both or neither. These terms can refer to either a
data set as a whole or an individual measurement.
Precision
 degree of exactness to which a measurement can be reproduced (consistency)
 limited by the smallest division on the measuring device
 example: The smallest division on a meter stick is a millimeter
Accuracy
 extent to which a group of data agrees with the accepted value
 usually indicated by a percent error calculation
Example one: Consider the targets below. If your ultimate goal is to hit the bulls-eye, are these shots:
1
1
2
3
3
2
2
1
3
1
A. Precise or Accurate?
B. Precise or Accurate?
C. Precise or Accurate?
3
2
D. Precise or Accurate?
For target “A”, the shots are relatively close together, however, they are nowhere near the bull’s-eye.
These shots would be considered “precise”, but NOT accurate.
For target “B”, the three shots are scattered and are therefore not precise. However, the average of the
data set is accurate.
For target “C”, all three shots landed in the bulls-eye region. Therefore, the shots are precise and all
three are accurate.
For target “D”, all three shots are scattered and are not near the bull’s-eye. The shots are neither precise
nor accurate.
Example two: A student is asked to measure the volume of a small steel ball. Which of the following
instruments would give the most precise measurement?
A.
B.
C.
D.
For precision, both the size of the device and the spacing of the unit divisions are important.
Therefore, the most precise measurement would be acquired with instrument “A”.
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Measurement: Estimation and Precision
How do you know the appropriate precision to use when making a
measurement?
How do you distinguish between measurements that are the same
and ones that are not?
Rules for estimation and precision

As a general rule, read and record measurements as precisely as possible. It is easier to
round off than to re-measure.

When using an analog scale (such as a meter stick, a graduated cylinder, a spring scale,
or a voltmeter), you should be prepared to estimate to one decimal place beyond the
smallest division. This is the MAXIMUM precision of the device.
Example: A ruler has ten divisions between 1 and 2 cm. You can estimate one decimal
place beyond the smallest division, or 0.01 cm. A typical reading could be 1.37 cm.

It is sometimes impractical or unnecessary to be that precise. In that case, be prepared
to justify the precision that you choose.
You use a meter stick outdoors to measure the length of a car. It is impractical to
measure to one decimal place beyond the smallest division of a millimeter under those
conditions. You would probably choose to measure to the nearest centimeter.

Sometimes you will be told the precision to which you should measure. Be sure to write
down those measurements appropriately.
When asked to measure the width of the lab table to the nearest centimeter, you record
36 cm, not 36.3 cm or 36.0 cm.

For digital readouts such as digital balances, realize that the last digit will usually vary by
at least ± one digit. Be prepared to justify your chosen precision.
If you measured the mass of the same object three times on a digital balance, it is
unlikely that you will have measurements that are exactly the same. Typical repeat
measurements might be 530.2g, 530.1g and 530.3g.
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