Significant Figures
(Sig Figs)
Quantity includes all known digits
plus one estimated digit = last digit
of #
Indicates precision
500 vs 500.01
1
Rule 1: All digits recorded from a lab
measurement are called significant figures.
Rule 2: All non-zero digits are considered
significant.
measurement
96 g
61.4 g
0.52 g
number of sig figs
_________
2
3
_________
_________
2
2
Rule 3: Middle zeros are always
significant. SANDWICH RULE
measurement
number of sig figs
4
5.029 m _________
3
306 cm _________
410.0 g _________
4
3
Rule 4: A leading zero is never significant.
The zeros are place holders only.
measurement
number of sig figs
1
0007 g
________
3
0.00783 kg ________
5.00783 kg ________
6
4
Rule 5: Trailing zeros are significant only
when to the right of decimal point.
measurement
number of sig figs
3
47200 km ________
5
4.7200 km ________
3
82.0 m
________
5
Rule 6: All significant figures include units.
Rule 7: All numbers multiplied by 10 in
scientific notation are considered significant.
measurement
number of sig figs
3.600 x 103 m _________
4
3
1.02 x 10-9 g _________
6
SAME RULES: SHORT CUT “The Arrow Rule”: Draw
an arrow to the first significant digit and count
significant figures.
Atlantic
Ocean
Pacific
Ocean
decimal Present
measurement
decimal Absent
# sig figs
measurement
# sig figs
61.4 g
____
3
306 cm
____
3
0.52 g
2
____
7 000 g
1
____
82.0 m
3
____
5
50 002 pennies ____
3
0.00783 kg ____
7
Practice: how many sig figs in each quantity?
45.35 km
6.2100 dag
1.22 us
8 000 000 m/s
0.034567 ML
____
4
5
____
____
3
1
____
5
____
8
# of sig figs in answer is based on # sig figs in
least precise measurement
Which is the least precise, 7.22 m or 7.22555 m?
7.22 m
_______
Rules for multiplication and division:
1) Count the # of sig figs in each measurement.
2) Use least # sig figs for # of digits in answer.
Examples:
4.5 cm X 2.54 cm X 3.215 cm = 75.8097 cm3
answer w/ sig figs _________
76 cm3
4.62 g
0.308 g/cm3
=
15.00 cm3
g/cm3
answer w/ sig figs 0.308
__________
2
2.124 mm X 65mm = 138.06 mm
140 mm2 or 1.4 x 102 mm2
answer w/ sig figs _____________________________
9
Rule for addition and subtraction:
Look for the last significant place; the answer
matches that last sig place.
Examples:
100.5 dm
+ 50 dm
150.5 dm
answer w/ sig figs
150 dm
_________
51.25 L
- 1.5 L
49.75 L
answer w/ sig figs
49.8 L
__________
10
Rule for addition and subtraction:
Look for the last significant place; the answer
matches that last sig place.
Examples:
25002 mm
105
mm
+ 4.25 mm
25111.25 mm
answer w/ sig figs
25111
mm
_________
1.520 g
2.15 g
+9.5515 g
13.2215 g
answer w/ sig figs
13.22 g
__________
11
Precision of equipment limits
accuracy of a measurement
100.5321
+ 50.4
150.9321
w/ sf 150.9
100.5321
+50.3572
150.8893
Answer with 1/10th
place precision is less
accurate.
Answer with 1/10,000th
place precision is more
accurate.
12