Tutorial 1 September 13th, 2001 Significant figures Number of ...

•1
Tutorial 1
September 13 th , 2001
Petrucci, Harwood and Herring
03/10/01 CHEM 1000B 3.0 Tutorial Gases 1
Significant figures
• If the problem is based on measured
experimental data, there is only one right
answer.
Example: 12.512 x 5.06 = 63.31072, 63.3107,
63.311 or 63 and why
03/10/01 CHEM 1000B 3.0 Tutorial Gases 2
Number of Significant Figures
7.5 x 10
3
7.50 x 10
m
3
7.500 x 10
3
m
m
2 significant figures
3 significant figures
4 significant figures
03/10/01 CHEM 1000B 3.0 Tutorial Gases 3

•2
In scientific notation: 4.004500 x 10 -3
03/10/01 CHEM 1000B 3.0 Tutorial Gases 4
Round-Off Errors
•Using sig. figs. properly avoid round-off errors
!if the last digit is 0 to 4, don’t change the
previous digit
!if it is 5 to 9, raise the previous digit by 1.
Example: if the correct number of sig. figs. is (2),
67.3 or 67.0 round off to 67
but 67.5 or 67.9 round off to 68
03/10/01 CHEM 1000B 3.0 Tutorial Gases 5
Example:
97x ½ x ½ x ½ = 97/8 = 12.125 or 12 (2 sig.figs)
97 x ½ = 48.5 = 49
49 x ½ = 24.5 = 25
25 x ½ = 12.5 = 13 (2 sig. Figs.)
03/10/01 CHEM 1000B 3.0 Tutorial Gases 6

•3
Exact Numbers and Physical Constants
•When we find ½ of a number, we mean x
0.50000000…; the ½ is know to an infinite number
of sig. Figs., and doesn’t affect the number of sig.
Figs. In the answer.
Such exact numbers are often present in
formulae; e.g. kinetic energy KE = ½ mν 2
This is true also for π = 3.141592654… as in the
area of a circle A = π r 2
03/10/01 CHEM 1000B 3.0 Tutorial Gases 7
•Even the common physical constants
e.g. the gas constant R = 8.31451 J mol -1 K -1 =
0.0820584 L atm mol -1 K -1
are known to enough sig. figs. so that they seldom
limit the number of sig. figs. in the answer.
Use all the available digits in your calculations.
03/10/01 CHEM 1000B 3.0 Tutorial Gases 8
In practice, the correct handling of sig. figs. can be taken
care of by a few simple Rules.
1. Put all the data into the calculation using all the digits
you’ve got.
2. When you multiply and/or divide numbers, it is the
number with the fewest sig. figs. which controls the
answer.
3. When you add and/or subtract numbers, it is the number
with the fewest decimal places which controls the
answer.
03/10/01 CHEM 1000B 3.0 Tutorial Gases 9

•4
Significant figures
• If the problem is based on measured
experimental data, there is only one right
answer.
Example: 12.512 x 5.06 = 63.31072, 63.3,
63.311 or 63 and why
Answer: 12.512 x 5.06 = 63.3 (3 sig. figs)
5 sig. figs
3 sig. figs
03/10/01 CHEM 1000B 3.0 Tutorial Gases 10
The 1.000 kg red cylinder
has a diameter of 4.10 cm. What
pressure, expressed in Torr, does
this cylinder exert on the surface
beneath it
What substance is this
cylinder made of, could it be Hg
03/10/01 CHEM 1000B 3.0 Tutorial Gases 11