CHEMISTRY P
MRS. EDWARDS, MR. HAMM, MR. NELSON, DR. SELGRATH
NAME:
FALL 2013
HANDOUT #2: SIGNIFICANT FIGURES
Measurements performed in the laboratory are recorded with a certain degree of uncertainty—all measurements are
approximations limited in precision by the measurement instrument involved, and limited in accuracy by the skill of
the experimenter. The latter can be remedied by practice, and therefore, may soon be dismissed, but the former will
always exist. To convey the degree of uncertainty in a measurement, the experimenter records enough digits such
that the last digit recorded is the only one that is uncertain, but not completely unknown. For example in the
measurement 2.50  0.01; the hundredth's place is uncertain. This last decimal place is called the least significant
decimal place, and the numeral in it is called the least significant digit.
This is a convention universally embraced by the scientific community. When you have mastered the following rules
for representing measurements, you will know how to record measurements and the answers to calculations, and
well as interpret the data and calculations of others.
RULES FOR DETERMINING THE NUMBER OF SIGNIFICANT FIGURES IN A MEASUREMENT:
1. All digits other than zero are significant.
2. Zeros between non-zero digits are significant.
3. Final zeros to the right of a decimal point are significant.
4. In numbers smaller than one, zeroes directly to the left or directly to the right of the decimal point are
not significant.
Examples:
6100 m = 2 significant figures
6010 m = 3 significant figures
61.00 m = 4 significant figures
0.061 m = 2 significant figures
(rule 1)
(rule 2)
(rule 3)
(rule 4)
Another way of looking at it…
All digits are significant except for zeros in these two cases:
1. Zeros to the right of the last non-zero digit in whole numbers (‘trailing’ zeros).
2. Zeros to the left of the first non-zero digit in numbers smaller than one (‘leading’ zeros).
Examples: (Underlined digits are significant. Any zeros not underlined are not significant)
75000 (2 sig figs)
18600 (3 sig figs)
220 (2 sig figs)
3050 (3 sig figs)
0.826
0.00125
0.00041
0.03200
(3 sig figs)
(3 sig figs)
(2 sig figs)
(4 sig figs)
PROBLEMS: Determine the number of significant figures in each of the following measurements.
1.
2.
3.
4.
5.
5.730 m
8.765 m
0.00073 m
40.007 m
3000 m
© BHS Chemistry, 2013
6.
7.
8.
9.
10.
50700 m
0.070020 m
0.010 m
310 m
3.10 x 10² m
CHEMISTRY P
MRS. EDWARDS, MR. HAMM, MR. NELSON, DR. SELGRATH
NAME:
FALL 2013
RULES FOR DETERMINING THE NUMBER OF SIGNIFICANT FIGURES IN THE ANSWER AFTER PERFORMING
A CALCULATION:
FOR MULTIPLICATION AND DIVISION: The answer (either the product or quotient) should be rounded as
to have the same number of significant figures as the factor having the least number of significant
figures.
FOR ADDITION AND SUBTRACTION: The answer (either the sum or difference) should be rounded as to
have its least significant decimal place the same as that of the quantity having the least significant
decimal place.
Examples:
3.41 (3 sig fig)
x 2.8
(2 sig fig)
9.548 answer must have smaller number of significant figures; round answer
to 2 sig figs.
9.5
(answer)
27.23 (hundredths place sig)
- 12.5
(tenths place sig)
14.73 answer must have least significant decimal place; round answer to
tenths place.
14.7 (answer)
PROBLEMS: Perform the following calculations, leaving your answer written with the appropriate number of
allowable significant figures.
11. (8.3)(1.22)
12. (1.8 x 10–3)(2.9 x 10–2)
13. (8432)
(12.5)
14. (5.3 x 10–2)
(0.255)
15. (8.40)
(0.7)
16.
17.
18.
19.
20.
61.2 + 9.35 + 8.6
9.44 – 2.111
1.36 + 10.17
34.61 – 17.3
45.2 + 230 + 7.820
21.
22.
23.
24.
25.
(5.50)(0.098)
(680)  (24.0)
36.5 + 9.04 – 0.342
(0.00208)(4.11 x 10–2)
250 – 18
© BHS Chemistry, 2013