SIGNIFICANT FIGURES
Numbers that express measurements always contain one or more digits we are certain of,
plus one that is estimated. All of these digits, the certain ones and the estimated one, are
considered to be reasonably reliable, and are called significant figures.
For example, a reading on a graduated cylinder of 36.0 mL contains three significant figures, the first
two of which are certain (obtained from reading the physical graduations on the graduated cylinder),
and the last of which is estimated (obtained from reading between graduations). The last digit of any
measurement is considered to be significant although it is also estimated.
When numbers do not contain zeros, there is no question about the significance of each digit.
Nonzero digits are all significant because scientists would not write them down if they were
not read as parts of a measurement. Sometimes, however, zeros are used to indicate the
size of a number. For example, if the mass of an elephant is given as 11,000 kilograms, we
are not certain whether the elephant has a mass of exactly 11,000 kg or approximately
11,000 kg. The latter is probably true, because a balance delicate enough to mass to the
nearest kg is unlikely to be used to weight such a large quantity. In writing 11,000, the zeros
are used to show that the 11 is 11 thousands To eliminate confusion on whether zeros are
significant scientists have agreed upon certain guidelines to communicate which digits in a
measurement are significant.
DETERMINING THE NUMBER OF SIGNIFICANT FIGURES (Significant figures are bolded)
1. Nonzeros: All nonzero digits in measurements are significant.
5.34 cm = 3 significant figures
15.4 km = 3 significant figures
2. Zeros
a. Zeros at the beginning of a number are never significant. They only hold the place of the digits.
0.0034 = 2 significant figures
0.02232 = 4 significant figures
b. Zeros between two nonzero digits are always significant.
0.305 = 3 significant figures
0.005061 = 4 significant figures
c. Zeros at the end of a nondecimal number are not significant. The zeros only hold the place of the
other digits.
26,000 = 2 significant figures
150 = 2 significant figures
d. Zeros at the end of a decimal number are always significant. They would not be added unless they
were intended to be significant.
520.00 = 5 significant figures
0.034900 = 5 significant figures
3. Scientific Notation: All digits of numbers written in scientific notation are significant.
3.56 x 10-4 = 3 significant figures
1.031 x 107 = 4 significant figures
Exercises: Underline the significant figures in each of the following.
a. 34.590 mm
f. 150. L
k. 10000 km
b. 4590.0909 km
g. 6.02 x 1023 sec
l. 10.03040 km
c. 14.00 g
h. 459.34 g
m. 0.00301 g
d. 0.00340 kg
i. 30 mL
n. 0.001 L
e. 5.200 m
j. 1.34 centimeters
o. 0.001000 sec
Answers: (a) 5; (b) 8; (c) 4; (d) 3; (e) 4; (f) 3; (g) 3; (h) 5; (i) 1; (j) 3; (k) 1; (l) 7; (m) 3; (n) 1; (o) 4.