# How do you write 0.000000001 in scientific notation?

Jan 3, 2017

$1.0 \times {10}^{-} 9$

#### Explanation:

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

$0.000000001 = 1.0 \times {10}^{-} 9$

Jan 3, 2017

$1.0 \times {10}^{- 9}$

#### Explanation:

$\textcolor{b l u e}{\text{Perhaps 'splitting hairs'}}$

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 $1.0 \times 10$ 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 $10.0 \leftarrow \text{ movement of numbers is 1 place}$

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$\textcolor{b l u e}{\text{Answering the question}}$

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 $\frac{1.0}{10} ^ 9 = 0.000000001$

But another way of writing $\frac{1}{10} ^ 9 \text{ is } {10}^{- 9}$ so we end up with the form:

$1.0 \times \frac{1}{10} ^ 9 = 1.0 \times {10}^{- 9}$