Writing numbers that are very big or very small ...

In science, you will encounter numbers that are very big or extremely small. These can be rather inconvenient to write out in the normal notation. Powers of ten is a useful shorthand method of writing very large or very small numbers. For example,

One thousand (1000) is 10³ ; reads 'ten to the power 3' and is 1 followed by 3 zeros
One divided by 1000 is 0.001 or 10^-3 ; reads 'ten to the power minus 3'

And that is it - the positive power on ten tells us how many zeros are after 1.
negative powers of ten tell us the position of the 1 after the decimal point.

Distance of the Sun from the Earth is 150 million km or 150,000,000 km or 15 x 10⁷ km.
Diameter of an atom is 0.0000000002 m or 2 x 10^-10 m.

Multiplication and division of powers of ten numbers is very easy...

When you multiply two numbers powers add

When you divide two numebrs powers substract.

Example: Multiply 2 million by 4 million

Longhand: 2,000,000 x 4,000,000 = 8,000,000,000,000

Powers of ten: 2 x 10⁶ x 4 x 10⁶ = 8 x 10¹²