Question

How do you write `0.000439` in scientific notation?

Answer 1

`4.39 * 10^-4`

Explanation:

Scientific notation basically just uses exponents with base 10 to make representing either super large or infinitesimally small numbers a lot easier. It can get confusing, but here's the key:

Any number in scientific notation will have something times 10 to some power (let's say `m`). To get the original number, just move `m` decimal places up or down (based on the sign).

For example, `3.6 * 10^10` means that you move up 34 decimal places (to 36000000000), and conversely, `3.6 * 10^-10` means you move back 34 decimal places (to 0.00000000034). You also now see why scientific notation is useful in practice -- you'll often get ridiculously large or small numbers like that, and it would be a pain to write all those zeroes over and over again!

This also works when you want to convert a number into scientific notation: we move up or down until we have one whole number followed by how many ever decimal places deemed appropriate.

Consider your example: `0.000439`. To get to a whole number, I need to move my decimal place up by 4 spots. So, I'd end up having `4.39 * 10^-4`.

Note that based on the number of significant digits you need, you can round that up to `4.4* 10^-4`, or down to `4.390* 10^-4` as needed. This is actually a very common reason why you'll want to use scientific notation -- it works great with sig figs.

If you need additional help, this fantastic video by Tyler DeWitt should clear things up for you.

Hope that helps :)