ACTIVITY 1-1 Scientific Notation and The Speed of Light
Radio waves, like all electromagnetic waves, travel at the speed of light – 300 000 000 meters
per second (3 hundred million meters per second). The speed of light is obviously a large
number. In working with this number, and other large numbers, it is convenient to express it in
scientific notation. In scientific notation, powers of ten are used to represent the zeroes in large
numbers. The following table shows how this is done.
Number
Name
Power of ten
1
one
100
10
ten
101
100
hundred
102
1000
thousand
103
10000
ten thousand
104
100000
hundred thousand
105
1000000
million
106
10000000
ten million
107
100000000
hundred million
108
1000000000
billion
109
If you examine the first and last columns, you can see that the power of ten is the same as the
number of zeroes in the number. So the speed of light, which is 3 followed by 8 zeroes, becomes
3 x 108 meters per second. The standard symbol for the speed of light is c, so we can write:
c = 3 x 108 m/s
Since radio waves travel at a constant speed, the distance traveled is given by:
distance = speed times time
or d = c t
where d = distance in meters
t = time in seconds
c = 3 x 108 meters per second
Example Problem: How far does a radio wave travel in 5 minutes?
t = 5 min = 5(60) = 300 s = 3 x 102 s
c = 3 x 108 m/s
d = ? m
d = c t
d = (3 x 108) (3 x 102)
d = (3 x 3) x 108+2
d = 9 x 1010 m
RULE: to multiply,
MULTIPLY the numbers,
ADD the powers of ten
