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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 =
  10^{6 - 3} =
  10³ =
  1,000.

• Also, the zeros can then be used for significant figures.

Links

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

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 × (×) x symbols to × (×), and upgraded HTML,
               to work around a reported Mac Netscape problem.
               Fixed ChemTeam link.
  1998.Sep.22  Added link to `how to write' in Links section.
               Added this History section.
  1997.summer  Created.