27
Self-Check
Suppose you could slow down time so that according to your perception, a
beam of light would move across a room at the speed of a slow walk. If you
perceived a nanosecond as if it was a second, how would you perceive a
microsecond.
0.8Scientific Notation
Most of the interesting phenomena our universe has to offer are not on
the human scale. It would take about 1,000,000,000,000,000,000,000
bacteria to equal the mass of a human body. When the physicist Thomas
Young discovered that light was a wave, it was back in the bad old days
before scientific notation, and he was obliged to write that the time required
for one vibration of the wave was 1/500 of a millionth of a millionth of a
second. Scientific notation is a less awkward way to write very large and
very small numbers such as these. Here’s a quick review.
Scientific notation means writing a number in terms of a product of
something from 1 to 10 and something else that is a power of ten. For
instance,
32 = 3.2 x 10
1
320 = 3.2 x 10
2
3200 = 3.2 x 10
3
...
Each number is ten times bigger than the previous one.
Since 10
1
is ten times smaller than 10
2
, it makes sense to use the
notation 10
0
to stand for one, the number that is in turn ten times smaller
than 10
1
. Continuing on, we can write 10
-1
to stand for 0.1, the number
ten times smaller than 10
0
. Negative exponents are used for small numbers:
3.2 = 3.2 x 10
0
0.32 = 3.2 x 10
-1
0.032 = 3.2 x 10
-2
...
A common source of confusion is the notation used on the displays of
many calculators. Examples:
3.2 x 10
6
(written notation)
3.2E+6(notation on some calculators)
3.2
6
(notation on some other calculators)
The last example is particularly unfortunate, because 3.2
6
really stands
for the number 3.2x3.2x3.2x3.2x3.2x3.2 = 1074, a totally different number
from 3.2 x 10
6
= 3200000. The calculator notation should never be used in
writing. It’s just a way for the manufacturer to save money by making a
simpler display.
A microsecond is 1000 times longer than a nanosecond, so it would seem like 1000 seconds, or about 20 minutes.
Section 0.8Scientific Notation