How do you know where to put the decimal point when doing scientific notation?

The idea behind scientific notation is to be able to write a large as small as humanly possible. As such, you're going to want to place the decimal where it would allow the number to be small.

Take the number 23,000,000,000, a very uncomfortable number to write out. It is true, in any case, that the number could be written as 23,000 x 10^6, or any combination of these two, but this would not minimize the space taken. In order to use the least amount of space, the decimal must come directly after the first digit.

As such, our previous example would be written, 2.3 x 10^9.
Hope this helps :)

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