Industrial Electricity
HANDOUT #1: Scientific Notation & Metric Prefixes
SCIENTIFIC NOTATION
It is often cumbersome to work with extremely large and/or extremely small numbers.
For example:
2,300,000,000 x 0.000,000,000,041 = ???
An effective method for dealing with these types of numbers is to first convert them to scientific notation and then
apply the rules related to exponents that you likely learned in a math class along the way.
The first rule for converting a number to scientific notation is to reposition the decimal such that it falls just to the
right of the first non-zero digit of the number. For the number 2,300,000,000 this would become:
2,300,000,000  2.300000000
But notice that I have made the number MUCH smaller than it was before. To compensate for that, I must “add” a
times-ten (X 10n) exponent to the new number. In doing so, the number will be exactly the same value as it was
before, though clearly the way it looks will have changed. Since, in this case, I have made the number much
smaller, I need to use a positive (+n) exponent. The number that I put in for ‘n’ is the number of places that I
moved the decimal. But where is the decimal in the original number? Well, since it’s not explicitly written, it’s
implied to be just to the right of the last zero. Go ahead and pencil it in above; just to the right of the last zero and
to the left of the arrow. Now use your pencil to count how many places you moved the decimal. I count nine
places. So, the “new” number becomes:
2,300,000,000  2.3 X 109
Notice that all of the zeros were eliminated. Often, when converting to scientific notation, you only keep the nonzero digits of the number. This is not always true, as in the case of a chemistry or physics class.
Now let’s do the same thing for the number 0.000,000,000,041. First, move the decimal to fall between the 4 and
the 1:
0.000,000,000,041  000000000004.1
In this case I have taken a really small number and made it MUCH larger. To compensate for that, and keep the
number the same value, I must, again, use a (X 10n) exponent. This time the exponent must be negative. It’s
important to note that negative exponents indicate small numbers, NOT negative numbers. What value of ‘n’ do I
use? Again, count how many places the decimal point has been moved. I count eleven. So, the number becomes:
0.000,000,000,041  4.1 X 10-11
Now take a look at the example again, this time using the scientific notation version of the numbers.
(2.3 X 109) x (4.1 X 10-11) = ???
One of the rules of handling exponents states that when multiplying two numbers together, add the exponents. So,
in this case, we have: 9 + (-11) = -2. Then simply multiply together the “regular” numbers: 2.3 x 4.1 = 9.43. So, in
the end, we have:
(2.3 X 109) x (4.1 X 10-11) = 9.43 x 10-2
Another rule for the handling of exponents says that when dividing two numbers, subtract the exponents.
For example:
950,000 / 0.0013 = ???
Using the rules outlined above for converting decimal numbers to scientific notation, we have
(9.5 X 105) / (1.3 X 10-3) = ???
Subtracting the exponents gives: 5 – (-3) = 8. And, dividing 9.5 by 1.3 gives 7.3. So, the result is
(9.5 X 105) / (1.3 X 10-3) = 7.3 X 108
METRIC PREFIXES
In science, certain powers of ten are favored over others. These favored powers are given prefixes (names) and
symbols (the abbreviation for the prefixes). Often, once a number has been converted to scientific notation, it is
again converted to one of these favored powers of ten. In electricity and electronics, a subcategory of these favored
powers is used. Below is a list of common metric prefixes. The ones often used in electricity and electronics are in
bold print.
METRIC PREFIXES
Multiple
1024
1021
1018
1015
1012
109
106
103
102
101
Prefix
yotta
zetta
exa
peta
tera
giga
mega
kilo
hecto
deka
Symbol
Y
Z
E
P
T
G
M
k
h
da
Multiple
10-1
10-2
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
Prefix
deci
centi
milli
micro
nano
pico
femto
atto
zepto
yocto
Symbol
d
c
m
μ
n
p
f
a
z
y
Using the results from the two previous examples, let’s see how a number in scientific notation can be converted to
a number with a metric prefix. Let’s, for the sake of argument, say the first result (9.43 x 10-2) is number that
represents a measured voltage. Voltage, if you are not familiar, can be thought of as the force that causes electricity
to flow through a wire in an electrical circuit. So we would say that the voltage is 9.43 X 10-2 volts. Notice that the
power, 10-2, is close to one of the favored powers used in electricity, namely 10-3. Notice further that 10-3 is a factor
of ten smaller than 10-2. If we want to use 10-3 as the exponent rather than10-2, we must compensate by making the
number portion (9.43) larger by a factor of ten. Putting these steps together we have:
9.43 x 10-2 volts = 94.3 x 10-3 volts
Of course the whole reason for doing this is to be able to use the metric prefix rather than the power-of-ten
exponent. Since 10-3 means the same thing as the prefix “milli” we can write the voltage as 94.3 millivolts or, using
the prefix’s abbreviation, simply 94.3mV. Note that there is nothing particularly special about using the milli
prefix except that it is closest to the scientific notation version of our number. We could have used the “micro”
prefix and written the number as 94300μV (try it!) but now the number itself is become larger and more
cumbersome again.
Try the process with the second result by converting it to 10 9 and using the “Mega” prefix or more correctly, the
abbreviation for the metric prefix. You should get 0.73GV. How? The Giga (G) prefix (109) is one factor of ten
larger than then that of the number itself (7.3 x 108). To compensate for making the exponent larger by a factor of
ten, the number must become smaller by a factor of ten. So we have:
7.3 x 108 volts = 0.73 x 109 volts = 0.73 gigavolts = 0.73GV