Standard form is a way of writing down very large or very
small numbers easily and without using lots of zeros. We sometimes call it scientific
notation.

We write 1000 as 10^{3}, 10 000 as 10^{4} and so
on.

Small numbers can also be written in standard form. However, instead of the
index of the power being positive it will be negative.

So 0.001 is written as 10^{-3}

5000 would be 5x10^{3}

0.005 would be 5x10^{-
3}

5200 would be written as 5.2x10^{3}

0.0052 would be written as
5.2x10^{-3}

Rules for the use of standard form**Addition
or subtraction**

5000 + 3000 = 5x10^{3} + 3x10^{3} =
8x10^{3}

0.001 + 0.002 = 1x10^{-3} + 2x10^{-3} =
3x10^{-3}

Don't forget here that 10^{3} is actually
1x10^{3}

5000 + 400 = 5x10^{3} + 4x10^{2} = 5x10^{3}
+ 0.4x10^{3} = 5.4x10^{3}

Notice what I have done to the 400 to
make both terms raised to 10 to the power 3.

3000 - 2400 = 3x10^{3} -
2.4x10^{3} = 0.6x10^{3} = 6x10^{2} = 600**Multiplication
or division**

(add or subtract the indices)

5000 x 3000 = 5x10^{3} x
3x10^{3} = 15x10^{6} = 1.5x10^{7}

50000/300 =
[5x10^{3}]/[3x10^{2}] = 1.67x10^{2} = 167

Standard
form is very useful when you are dealing with numbers like the charge on an electron
(1.6x10^{-19} C) or even worse Planck's constant (6.63x10^{-34}
Js).

Imagine having to write these as:

Electron charge = 0.000 000 000
000 000 000 16 C

Planck's constant = 0.000 000 000 000 000 000 000 000 000
000 000 663 Js