Question

How do you write `0.000000001` in scientific notation?

Answer 1

`1.0 xx 10^-9`

Explanation:

Because we need to move the decimal point 9 places to the right, the exponent for the `10`s term will be negative:

`0.000000001 = 1.0 xx 10^-9`

Answer 2

`1.0xx10^(-9)`

Explanation:

`color(blue)("Perhaps 'splitting hairs'")`

Some people state "move the decimal point"

I state "fix the decimal point and move the numbers".

Reason:

Consider the value 1.0
Now consider the modification `1.0xx10` you have changed from counting in units to counting in tens. Consequently the number shifts to the left by 1 place and you insert the place keeper of 0 giving `10.0 larr" movement of numbers is 1 place"`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

The target for this number is to end up with `1.0`

But 1.0 is not the same value we started with. So we need to include (without applying it) a correction so that the actual overall value becomes the same.

So we have `1.0/10^9 = 0.000000001`

But another way of writing `1/10^9" is "10^(-9)` so we end up with the form:

`1.0xx1/10^9=1.0xx10^(-9)`