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
...