What is exponential notation?

Answer 1

Exponential Notation

2 × 105

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?

  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).

Links

An Exponential Notation Meta Page

See also the links in Scientific Notation .

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