Chapter 3: Measurement: Sigfigs
Objectives
• Determine the number of significant figures
in a measurement and in a calculated
answer
Olympic 100 Meter Results ‘48-60
•
•
•
•
1948
– GOLD Harrison Dillard, USA
– SILVER Barney Ewell, USA
– BRONZE Lloyd LaBeach, PAN
Time
10.3
10.4
10.4
1952
– GOLD Lindy Remigino, USA
– SILVER Herbert McKenley, JAM
– BRONZE Emmanuel Bailey, GBR
10.80
10.83
1956
– GOLD Bobby Morrow, USA
– SILVER Thane Baker, USA
– BRONZE Hector Hogan, AUS
10.62
10.77
10.77
1960
– GOLD Armin Hary, GER
– SILVER David Sime, USA
– BRONZE Peter Radford, GBR
10.32
10.35
10.42
10.79
Uncertainty in measurements
• All measurements are limited by the
equipment and/or people performing the
measurement
• Data must express the uncertainty caused
by how it was obtained/measured
– First, we must know how to properly measure
using the tools given to us.
– Second, we must understand significant
figures in order to properly express the
uncertainty to others
Proper measurement
• Always
measure one
more digit than
your tool
allows
• The last digit
in a
measurement
is always
uncertain
Sigfig rules: counting
• Nonzero integers always count as a sigfig
– 47.9 has 3 sigfigs
• Leading zeros do not count as sigfigs
– 0.076 has 2 sigfigs
• Captive zeros count as sigfigs
– 1703 has 4 sigfigs
– 1.0008 has 5 sigfigs
• Trailing zeros only count if they come after a
decimal
– 9300 has 2 sigfigs
– 74.00 has 4 sigfigs
– 2.6180 has 5 sigfigs
Sigfig rules: exact numbers
• Sometimes, there are numbers which are
considered exact numbers
– Example: 2.54 cm = 1 in, exactly
• Exact numbers have an infinite number of sigfigs
– These include
• counts (counting 28 people in the room for example)
• exactly defined ratios such as the example above or something
like 60 min = 1 hr, 100 cm = 1 m, 5280 ft = 1 mi
Counting practice
How many significant figures in each of the
following?
1.0070 m  5 sig figs
17.10 kg 
4 sig figs
100,890 L 
5 sig figs
3.29 x 103 s 
3 sig figs
0.0054 cm 
2 sig figs
3,200,000 
2 sig figs
Sigfig rules: multiplication/division
• The number of sigfigs allowed in the result is
the same as the least precise measurement
(the one with the least sigfigs) in the
calculation.
• Example: 2.0 x 6.38 = 12.76 (4 sigfigs)
– 2.0 has 2 sigfigs
– 6.38 has 3 sigfigs
– The least precise measurement has 2 sigfigs so
the answer must be rounded to 2 sigfigs
– The correct answer is 13 (2 sigfigs)
Multiplication/division practice
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
23 m2
100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3
0.02 cm x 2.371 cm 0.04742 cm2
0.05 cm2
710 m ÷ 3.0 s
236.6666667 m/s
240 m/s
1818.2 lb x 3.23 ft
5872.786 lb·ft
5870 lb·ft
1.030 g ÷ 2.87 mL
0.358885017 g/mL
0.359 g/mL
Sigfig rules: addition/subtraction
• The number of decimal places in the result equals
the same number as the measurement with the
fewest decimal places.
– If there are no decimal places, then go with the
measurement with the fewest place values extending
right.
• Example: 6.8 + 11.934 = 18.734
– 6.8 has 1 decimal place
– 11.934 has 3 decimal places
– The measurement with the fewest decimal places has 1,
so the answer must be rounded to 1 decimal
– The correct answer is 18.7 (1 decimal place)
Addition/subtraction practice
Calculation
Calculator says:
Answer
3.24 m + 7.0 m
10.24 m
10.2 m
100.0 g - 23.73 g
76.27 g
76.3 g
0.02 cm + 2.371 cm
2.391 cm
2.39 cm
710 L - 3.872 L
706.128 L
710 L
1818 lb + 3.37 lb
1821.37 lb
1821 lb
2.030 mL - 1.870 mL
0.16 mL
0.160 mL