Math Operations in Scientific Notation
11
The use of these rules in problems requiring both multiplication and division
is illustrated in the following example.
PROBLEM:
Use exponents to solve
2,000,000 x 0.00004 x 500 9
0.008 x 20
SOLUTION:
First, rewrite all numbers in standard scientific notation:
2,000,000 = 2 x 10
6
0.00004 = 4 x 105
500 = 5 x 10
2
0.008 = 8 x 10~
3
20 = 2 x 10
1
This gives
2 x 10
6 x 4 x 1Q5 x 5 x 10
2
8 x 10~
3 x 2 x I0
1
Dealing first with the lefthand factors, we find
2x4x5 = 5
8x2 ~ 2 ~ '
The exponent of the answer is
106 v in-' v 102
ine-5+2
ins
IU X 1U
X IU _ 1U
=
1U
_ JQ3-(-2) _ 1Q3 + 2 _ JQ5
10~
3 x 10
l
103+1
10~
2
The complete answer is 2.5 x 10
5 , or 250,000.
Approximate Calculations
Trained scientists often make mental estimates of numerical answers to quite
complicated calculations, with an ease that appears to border on the miraculous. Actually, all they do is round off numbers and use exponents to reduce the
calculation to a very simple form. It is quite useful for you to learn these
methods. By using them, you can save a great deal of time in homework
problems and on tests, and can tell whether an answer seems reasonable (i.e.,
whether you've made a math error).