Biology 12

Appendix 3 • MHR 553

3

APPENDIX

In order to conduct experiments in biology and
other sciences, you need to make measurements
and manipulate numbers. However, there is
always some degree of uncertainty in each
measured value that you record. Scientists
around the world have agreed that a
measurement should include the number of
digits that reasonably indicate its certainty. In
general, a measurement includes all digits that
are certain, and one final digit that is estimated
(uncertain). Together, these digits are called
significant digits.
For example, suppose you take a temperature
reading using two different thermometers, as
shown in Figure A3.1. The thermometer on
the left has gradations of 0.1°C. Reading the
thermometer carefully, you can be certain that
the mercury is above 32.3°C. To report your
measurement correctly, you must estimate the
final digit. You might estimate 32.33°C, as
shown in the diagram. Another person might
estimate 32.35°C. The final digit is uncertain.
On the other hand, the thermometer on the
right has gradations of 1°C. In this case, you
can be certain that the mercury is above 32°C,
but again you must estimate the final digit to
report your measurement correctly. The
diagram shows an estimate of 32.3°C.
A measurement of 32.33°C is more precise
than a measurement of 32.3°C. The first

measurement has four significant digits, while

the second measurement has only three.

Which Digits Are Significant?

In the previous example, the number of

significant digits was equal to the total number

of digits. Notice that the measurements did not

contain any zeros. When a value does not

contain any zeros, the number of significant

digits is equal to the total number of digits in

the value.When a value does contain one or

more zeros, however, determining the number

of significant digits requires more thought.

Zeros may or may not be significant depending

on where they are located. The rules used to

determine whether zeros in a quantity are

significant are as follows.

1.Zeros to the right of a quantity that includes

a decimal point are significant. Therefore,

7.50 mg has three significant digits.

2.Zeros located between two non-zero

numbers are significant. Therefore, 909 g

has three significant digits.

3.Zeros that are located to the left of a value

are not significant. Therefore, 0.0001 mm

has only one significant digit.

4.Zeros at the end of a whole number are

ambiguous. For example, $1000 would be

considered to be exact; however, 5 000 000

bacteria is probably not exact.

Significant Digits

33

32

31

0 0

100

40

10

60

70

80

90

34

35

36

37

38

39

40

30

20

110

30

31

32

33

20

30

40

50

32.33° C 32.3° C

Figure A3.1 A temperature

measurement made using

the thermometer on the left

will have more significant

digits, hence more certainty,

than a measurement made

using the thermometer on

the right.