Biomedical Engineering Reference
In-Depth Information
Fig. 8.1
Measurement of
the length of an object with
a ruler with the smallest
division in centimeters
1
2
3
4
5
6
7
cm
To begin this discussion, let us ask: how to determine the length of the object of
Fig.
8.1
with a meter stick marked in centimeters? How many digits should be used
to write the result? Which of them are the significant digits?
Measure and write down the length of the object of Fig.
8.1
.
Possible readouts:
4.4 cm
4.5 cm
4.6 cm
Incorrect readouts:
4cm
4.55 cm
In these measurements the first reliable digit is the number 4. Now, the tenth of a
centimeter is said to be a doubtful digit, since there are no divisions in the scale to
serve as reference, and depends on the evaluation of the experimenter. Hence, the
first three readouts are correct if, to perform the measurement, one has in mind that
the last digit is an uncertain, unreliable digit. The fourth readout, done without any
decimal digit and the fifth, with two decimal digits, are both wrong, in the first case
due to the lack and in the second case due to the excess of digits. This allows the
establishment of the correct form to express the result of a measurement. Therefore,
the result of a measurement must be written with all significant digits, composed of
reliable digits and only one estimated digit.
Now, do the same measurement with a meter stick, marked in millimeters, as
shown in Fig.
8.2
:
Possible readouts:
4.51 cm
4.53 cm
4.58 cm
Incorrect readouts:
4.5 cm
4.572 cm
Now the reliable digits are 4 and 5 and the hundredth of a centimeter is a
doubtful digit, which should be written, because it is also significant. The fourth
