Math and Measurements:
 Chemistry math is different from regular math
in that in chemistry we use measurements and
in math we use exact numbers. Because a
measurement is never 100% accurate (because
of sources of error), there is error to account
for. In order to make sure that the answers to
our mathematical problems are not more or less
accurate than the measurement involved, we
use sig figs.

 Precision
vs. Accuracy
 Precision: Ability to reproduce the same
result. Error in precision (Random Error)
occurs with poor technique
 Accuracy: Ability to get the correct result.
Error in accuracy (Systematic Error) occurs
with poor instrument (calibration).
 Ex.
A piece of metal is known to have a mass
of 18.01 g. When a student made three
attempts to determine the mass of the
metal, the following results were obtained:
a) 18.00 g b) 18.03 g c) 18.02 g
 Are these results accurate, precise, or both?
SI Units (Système International):
 Remember that Units are important! SI Units are
the units that are the most widely used units. SI
Units are base units. This means all other units
can be derived from the base SI Units.








Length- metre : m
Mass- kilogram: kg
Time- second: s
electric current- ampere: A
thermodynamic temperature- kelvin: K
amount of substance- mole: mol
luminous intensity- candela: cd
 How
to Measure:
 When measuring you always estimate
one digit.
 Example 1:
 Example
2:
 Significant
figures (sig figs) are the number
of digits in a number or measurement that
are meaningful. Sig figs are important in
order to calculate answers to problems using
measurements. Sig figs are used so that
when you are performing calculations using
measured values the answer is only as
accurate as the measurements used.
Sig figs rules:
1.
All non-zero digits are significant.
Ex. 384 has _______ sig figs
1.
All zeros between non-zero digits are significant.
Ex. 1,002 has ______ sig figs
1.
Zeros before the first non-zero digit are not
significant
Ex. 0.0020901 has ______ sig figs
1.
Zeros after the last non-zero digit may be
significant (they are significant if the number has a
decimal).
Ex. 0.00200 has _______ sig figs
Ex. 200
has ______ sig figs

 Note:
If you want the zeros after the last
non-zero digit to be significant, you should
write the number in scientific notation. For
example if 200 should have 3sig figs instead
of 1, it should be written as 2.00 x 102
 Examples:

315=
 305=
 300=
 300.=
 0.135=
 0.1350=
 0.01350=
 0.013050=
 Calculations
with sig figs:
 Adding and Subtracting with Sig Figs
 When adding and subtracting, the answer
will have the same number of decimals or
places as the digit with the least number
of decimals/places.
 Examples:


0.135 + 0.01 =
350 + 315 =
 Multiplying
and Dividing with Sig Figs
 When multiplying and dividing with sig
figs, the answer will have the same
number of sig figs as the number in the
question with the least number of sig figs.
 Example:

0.43986 x 0.10 =
 When
combining multiplying/dividing
with adding/subtracting
 Use BEDMAS and do not round until the
end (just keep track of the number of sig
figs each number has using underlining of
subscripts)
 Example:

0.31 + 4.00 x 3.6498

Why don’t you round until the end?
[(1.35+4.36) x (0.970x4.31)] x [(6.71x 5.98) /
(0.10+3.31)]
[5.710 x 4.1807] x [40.1258 / 3.410]
23.8718 x 11.767097
=280.9018
=281
[(1.35+4.36) x (0.970x4.31)] x [(6.71x 5.98) /
(0.10+3.31)]
[5.71 x 4.18] x [40.1 / 3.41]
23.9 x 11.8
=282
 Work
on the Assignment at the back of your
booklet (pg 21/22)