Standard form

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 10³, 10 000 as 10⁴ 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 5x10³
0.005 would be 5x10^{- 3}
5200 would be written as 5.2x10³
0.0052 would be written as 5.2x10^-3

Rules for the use of standard form

Addition or subtraction
5000 + 3000 = 5x10³ + 3x10³ = 8x10³
0.001 + 0.002 = 1x10^-3 + 2x10^-3 = 3x10^-3
Don't forget here that 10³ is actually 1x10³
5000 + 400 = 5x10³ + 4x10² = 5x10³ + 0.4x10³ = 5.4x10³
Notice what I have done to the 400 to make both terms raised to 10 to the power 3.
3000 - 2400 = 3x10³ - 2.4x10³ = 0.6x10³ = 6x10² = 600

Multiplication or division
(add or subtract the indices)
5000 x 3000 = 5x10³ x 3x10³ = 15x10⁶ = 1.5x10⁷
50000/300 = [5x10³]/[3x10²] = 1.67x10² = 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