# How do you write 0.000000258 in scientific notation?

Jun 22, 2018

$2.58 \cdot {10}^{-} 7$

#### Explanation:

Our coefficient ($c$) needs to be between 1 and 10, but cannot be 10 ($1 \le c > 10$). To do this, let's move our decimal point 7 units to the right. Since we moved it to the right, we will have a negative exponent. This leaves us with our answer of $2.58 \cdot {10}^{-} 7$.

Jun 22, 2018

$2.58 \times {10}^{- 7}$

#### Explanation:

Given:

$0.000000258$

$\textcolor{b r o w n}{0.000000258 \text{ is the same value as all the following:}}$
$\textcolor{w h i t e}{\text{d}}$
$0.00000258 \times \frac{1}{10} ^ 1$
$\textcolor{w h i t e}{\text{d}}$
$0.0000258 \times \frac{1}{10} ^ 2$
$\textcolor{w h i t e}{\text{d}}$
$0.000258 \times \frac{1}{10} ^ 3$
$\textcolor{w h i t e}{\text{d}}$
$0.00258 \times \frac{1}{10} ^ 4$
$\textcolor{w h i t e}{\text{d}}$
$0.0258 \times \frac{1}{10} ^ 5$
$\textcolor{w h i t e}{\text{d}}$
$0.258 \times \frac{1}{10} ^ 6$
$\textcolor{w h i t e}{\text{d}}$
$\textcolor{b r o w n}{2.58 \times \frac{1}{10} ^ 7}$

Another way of writing $2.58 \times \frac{1}{10} ^ 7 \text{ is } 2.58 \times {10}^{- 7}$

$\textcolor{b r o w n}{2.58 \times {10}^{- 7} \leftarrow \text{ Scientific notation}}$

People do not state it like this but it is actually what is happening.
The decimal point stays where it is. At each stage you move the digits to the left by 1 place.

counting in unit's $\to \textcolor{w h i t e}{\text{ddddd}} 5.0$

counting in ten's $\to \textcolor{w h i t e}{\text{ddd.d}} 50.0$

counting in hundreds$\to \textcolor{w h i t e}{\text{d}} 500.0$