Common Mathematical Operations In Chemistry Worksheets With Answers Page 2
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14A-2
Appendix A
•
Common Mathematical Operations in Chemistry
Therefore, we have
ln A 5 2.303 log A
To find a natural logarithm with an electronic calculator, enter the number and
press the ln button. If your calculator does not have an ln button, enter the number,
press the log button, and multiply by 2.303.
Antilogarithms
The antilogarithm is the base raised to the logarithm:
antilogarithm (antilog) of n is 10
n
Using two of the earlier examples, the antilog of 3 is 1000, and the antilog of 2.931
is 853. To obtain the antilog with a calculator, enter the number and press the 10
x
button. Similarly, to obtain the natural antilogarithm, enter the number and press the
e
x
button. [On some calculators, enter the number and first press inv and then the log
(or ln) button.]
Using ExponEntiAl (sciEntific) notAtion
Many quantities in chemistry are very large or very small. For example, in the conven-
tional way of writing numbers, the number of gold atoms in 1 gram of gold is
59,060,000,000,000,000,000,000 atoms (to four significant figures)
As another example, the mass in grams of one gold atom is
0.0000000000000000000003272 g (to four significant figures)
Exponential (scientific) notation provides a much more practical way of writing
such numbers. In exponential notation, we express numbers in the form
A10
n
where A (the coefficient) is greater than or equal to 1 and less than 10 (that is,
1 A 10), and n (the exponent) is an integer.
If the number we want to express in exponential notation is larger than 1, the
exponent is positive (n 0); if the number is smaller than 1, the exponent is negative
(n 0). The size of n tells the number of places the decimal point (in conventional
notation) must be moved to obtain a coefficient A greater than or equal to 1 and less
than 10 (in exponential notation). In exponential notation, 1 gram of gold contains
5.90610
22
atoms, and each gold atom has a mass of 3.27210
g.
22
Changing Between Conventional and Exponential Notation
In order to use exponential notation, you must be able to convert to it from conven-
tional notation, and vice versa.
1. To change a number from conventional to exponential notation, move the decimal
point to the left for numbers equal to or greater than 10 and to the right for num-
bers between 0 and 1:
75,000,000 changes to 7.510
7
(decimal point 7 places to the left)
0.006042 changes to 6.04210
(decimal point 3 places to the right)
3
2. To change a number from exponential to conventional notation, move the deci-
mal point the number of places indicated by the exponent to the right for num-
bers with positive exponents and to the left for numbers with negative
exponents:
1.3810
5
changes to 138,000 (decimal point 5 places to the right)
8.4110
changes to 0.00000841 (decimal point 6 places to the left)
6
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