How to talk to scientists
All scientists have to use maths to help predict and analyse experimental results, so it makes sense that anyone learning maths should understand "Standard Form" also known as "Scientific Notation" which is what scientists themselves use.

Scientists deal with very large numbers:

The distance from the earth to the moon is approximately 384,000,000 metres.

 

...and with very small numbers:

The mass of an electron is approximately 0.000000000000000000000000000000091093897 Kilograms.

It's obviously not a good idea to try doing calculations with these numbers (even if you could find a calculator wide enough!).

So standard form was born. In standard form the numbers are written in this shorthand way:

Distance from the earth to the sun = 3.84 x 108 m

Mass of an electron = 9.1093897 x 10-31 Kg

How it Works

108 means 10 raised to the power 8 i.e. 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.

And 3.84 x 108 is means simply 3.84 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.

Which is the same as 384 with 6 zeros after it (but quicker to write and a lot less easy to miss a zero or add a zero by mistake).

"Why 6 zeros and not 8?" you are probably asking.......

This is because two of the 8 zeros have been taken up with the number 84 behind the decimal point.

2.35 x 104 is how the number 23500 is written in standard form - imagine shuffling the numbers one decimal place to the left 4 times starting with 2.35: first you get 23.5, then 235, then 2350, then 23500. Another way to see this is to imagine the decimal point jumping over the numbers to the right: when the decimal point has jumped over the 5 to give you 235. then the next time the decimal point jumps you need to be kind enough to add a 0 for it to jump over.

10-31 is 10 raised to the minus power 31 - this simply means that instead of adding zeros to the left of the decimal point, we add them to the right to end up with a very small number.

Hence 9.1093897 x 10-31 is actually the decimal point followed by 30 zeros followed by 91093897.

e.g. 2.35 x 10-4 is 0.000235 - when you have a negative power, the number of zeros is influenced by how many numbers you have at the left of the decimal point. In this example we have to shuffle the 2 to the right of the decimal point before we can start inserting zeros. Hence we end up with 30 zeros rather than 31. If you prefer to shuffle the decimal point then you need to let it jump to the left this time.

Remember that standard form only allows one number to appear before the decimal place (in the case of small numbers, this number is 0).

So, you can now talk the same language as the scientists but not use up all your pens and paper in the process (also, as mentioned earlier, you will not be as likely to make errors using standard form)

And that's all there is to it!