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Exponential Notation
2 × 105
 How to simplify a number How to write and speak the exponential notation Scientific Notation Counting by powers of ten
Sliding the decimal point.

Exponential notation lets you move the decimal point in a number.

It simplifies numbers by getting rid of zeros, and making math easier.

• Getting rid of zeros helps with big 100,000,000 and small 0.000,000,001 numbers.

1,000,000. can be rewritten as
1. × 106 with the 6 saying the decimal has moved 6 steps left.
0.001 can be rewritten as
1. × 10-3 with the -3 saying the decimal has moved 3 steps right.
1. × 100 is just 1., since 0 means the decimal hasn't been moved.

Three billion, 3,000,000,000. is just 3. × 109. (You can count the steps yourself!.)

• Doing math is easier because
you can add to do multiplication,
and subtract to do division.
 You see... 10a × 10b = 10 a + b 10a / 10b = 10 a - b
So... Whats a million divided by a thousand? ( Here is a list. )
1,000,000. / 1,000. =
106 / 103 =
106 - 3 =
103 =
1,000.

• Also, the zeros can then be used for significant figures.
Here are a few more examples (of little value).

An Exponential Notation Meta Page
How to write and speak the exponential notation
Order-of-magnitude calculation - a "you are already doing it" introduction.
ChemTeam: Significant Figures
Chemistry 151: Powers of Ten, Prefixes, Basic Calculator Usage

## Details

```10a × 10b = 10 a + b
10a / 10b = 10 a - b

(10a)+p = 10 a × p
(10a)-r = 10 a / r

(A × 10a) × (B × 10b) = (A × B) × 10 a + b
(A × 10a) / (B × 10b) = (A / B) × 10 a - b

(A × 10a)+p = A+p × 10 a × p
(A × 10a)-r = A-r × 10 a / r

(A × 10same) + (B × 10same) = (A + B) × 10same
(A × 10same) - (B × 10same) = (A - B) × 10same

(B × 10bigger) + (S × 10smaller) = B × 10bigger
(B × 10bigger) - (S × 10smaller) = B × 10bigger
(S × 10smaller) + (B × 10bigger) = B × 10bigger
(S × 10smaller) - (B × 10bigger) = -B × 10bigger

And if doing "order of magnitude calculation":10same + 10same ~= 10same
10same - 10same ~= don't do it
10bigger + 10smaller ~= 10bigger
10bigger - 10smaller ~= 10bigger

```

 A View from the Back of the Envelope Comments encouraged. - Mitchell N Charity )

```Doables:
This could use an overhaul.  And page of `how to' and examples.
Perhaps absorb sci note's links aswell.

History:
2002.Mar.05  Changed × (&#215;) x symbols to × (&times;), and upgraded HTML,
to work around a reported Mac Netscape problem.