Math in Chemistry
During this unit, we will discuss:
1. Metric System
2. Exponential or Scientific Notation
3. Significant Digits
4. Dimensional Analysis
Math in Chemistry
Basic Definitions (pg. 55)
Precision – the exactness of a
measurement or the closeness of agreement
of two or more measurements of the same
quantity.
Accuracy – how close a measurement is to
the true value of the quantity measured
Math in Chemistry
Math in Chemistry
Example: Suppose two sets of students were
measuring 36.0 mL of water. The following
is their data:
Group 1
Group 2
34.6 mL
35.9 mL
34.2 mL
36.0 mL
34.3mL
35.9 mL
Which group is precise?
Which group is accurate?
Math in Chemistry
Percent Error
- used to determine how close to the true
values, or how accurate, an experimental
value actually is.
% Error = Experimental – Accepted Value x 100
Accepted Value
Math in Chemistry
Significant Figures (pgs. 56 – 59)
Every measurement has some uncertainty to
it, and that uncertainty should be indicated.
Measurements are therefore reported as the
number of digits that are known accurately
plus the first uncertain digit (the doubtful
digit).
Math in Chemistry
Rules for significant figures:
1. Nonzero digits are always significant.
Ex: 45.6 m
2. Zeros between nonzero digits are
significant
Ex: 40.7 mL
3. Zeros in front of nonzero digits are not
significant.
Ex: 0.009587
Math in Chemistry
Significant Figures (continued)
4. Zeros both at the end of a number and to
the right of a decimal point are significant.
Ex: 85.00 g
5. The significance of numbers ending in
zero that are not to the right of the decimal
point can be unclear. They are significant
only if the number contains a decimal point.
Ex: 2000 m
or
200.0 m
Math in Chemistry
Significant Figures (continued)
6. Exact numbers have not uncertainty and
contain an infinite number of significant
figures. These relationships are definitions,
not measurements.
Ex: There are exactly 1000 mL in one
liter.
Math in Chemistry
Significant Figures (continued)
7. In exponential numbers, only the number
portion of the number may be used when
considering the number of significant
figures.
Ex: 1.03 x 1020
3 x 1030
(Exercise)
Math in Chemistry
Two quick rules can also be used:
1. If the number HAS a decimal point, start at
the first non-zero number and keep
counting.
Ex: 0.090 = 2 significant figures (bold)
Math in Chemistry
2. If the number DOES NOT HAVE a decimal
point, start counting at the first non-zero digit
and STOP counting at the last non-zero digit.
Ex: 20 400
3 sig figs (bold)
Math in Chemistry
Calculating with Significant Figures (pg 58)
1. Multiplication and Division
- use the same number of significant
digits as the term with the least number of
S.D.
Ex: 12.257 m ← 5 Sig Figs
x 1.162 m ← 4 Sig Figs
14,2426234 →Round off to 14.24 m2
Math in Chemistry
Calculating with Significant Figures
2. Addition and Subtraction
- use the number with the least amount of
columns to determine the significant figures
Ex:
3.95 g
2.879 g
213.6
g
220.429 g → Round to 220.4 g
Math in Chemistry
Calculating with Significant Figures
3. If a calculation has both
addition/subtraction and
multiplication/division, round after each
operation.
Math in Chemistry
Scientific Notation (pg. 62)
 Very large or very small numbers appear
frequently in chemistry. To make these
numbers easier to work with and
understand, scientific notation or exponential
notation is used.
Ex: 50,000,000 can be written as 5 x 107
The 7 tells us that the decimal point was
moved to the left seven times.
Math in Chemistry
Rules for writing numbers is exponential
form:
1. The exponent represents the number of places the
decimal point has moved.
2. If the number is greater than one, the exponent must be
positive.
3. If the number is less than one, the exponent is negative.
4. For this class, always shift the decimal point so that
there is one significant figure to the left of the decimal point.
5. Always show all significant figures.
Calculating with Exponents

Multiplication without a calculator
 Multiply
the “significant” portion
 Add the exponents
 Ex:
x = (1.00 X 103)(2.0 X 106)
Calculating with Exponents

Division
Divide the “significant” numbers
 Subtract the exponents

Ex: 6.00 X 105
2.00 X 109