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