Chemistry
Exponential Notation
Try
the following exercise for practice and review purposes.
If necessary, you may need to consult your math textbook or Appendix C,
on pages R56-R58 of your Chemistry textbook.
I will not spend much class time on this material.
So if you are confused with how to interpret Exponential or scientific
notation, please consult these resources first and then come and see me.
1.
Converting
exponential notation to plain numbers (decimal notation):
Examples: 3
x 103 = 3000
or
2.2 x 10-4 = 0.00022
Try these:
3.742 x 103 =
5.5 x 105 =
7.2
x 10-2 =
3.653 x 101 =
9.6
x 10-5 =
2.
Converting
decimal notation to exponential notation:
Examples: 10,000 = 1 x 104
or
0.0010034 = 1.0034 x 10-3
Remember that the first number of your answer (the
coefficient) is always a number between 1 and 10. Try these:
176 =
0.0176 =
186,251 =
0.0004 =
47,900 =
0.000000933 =
3.
Multiplication
of exponential numbers:
Example: (3
x 104) (4 x 102) = (3
x 4) x 10(4 + 2) = 12 x 106 = 1.2 x 107
*** Note that you multiply the coefficients
and add the exponents. Be
sure that the final answer is in correct scientific notation.
Try these:
(3 x 104) (2 x 106) =
(4 x 102) (1.5 x 103) =
(5 x 104) (6 x 106) =
(4 x 10-3) (6 x 105) =
4.
Division
of exponential numbers:
Example: (4 x 105) / (2 x 102)
= (4/2) x 10(5-2) = 2 x 103
***Note that you divide the coefficients and subtract
the exponents.
Try these:
(6 x 109) / (1.5 x 103) =
(9 x 107) / (2 x 106) =
(2 x 105) / (4 x 102) =
(8 x 105) / (2 x 10-2) =
5.
Addition
of exponential numbers:
Example: (4 x 103) + (2 x 102)
= 4000 + 200 = 4200 = 4.2 x 103
or
=
(40 x 102) + (2 x 102) = (40 + 2) x 102
= 4.2 x 103
***Note that the exponent must be the same before you
can add exponential numbers. You
may convert the numbers to decimal form or convert one of the numbers to have
the same exponent as the other. In
any case, be sure to put your final number in exponential notation.
Try these:
(4.2 x 105) + (2.3 x 105) =
(7.4 x 102) + (5.3 x 102) =
(1.2 x 101) + (2.0 x 102) =
(4.2 x 10-3) + (2.3 x 10-2) =
6.
Subtraction
of exponential numbers:
Example:
(4 x 103) - (2 x 102) = 4000 - 200 = 3800 = 3.8 x
103
or
=
(40 x 102) - (2 x 102) = (40 - 2) x 102
= 3.8 x 103
***Note: As with addition, the exponent must be the
same before you can subtract exponential numbers. You may convert the numbers to decimal form or convert one of
the numbers to have the same exponent as the other. In any case, be sure to put your final number in exponential
notation.
Try these:
(3.8 x 103) - (2.1 x 103) =
(4.5 x 103) - (6.2 x 103) =
(5.5 x 103) - (4.2 x 102) =
(4 x 10-2) - (2 x 10-1) =
