# How do you write 0.000559 in scientific notation?

May 16, 2018

$5.59 \cdot {10}^{-} 4$

#### Explanation:

You just move your decimal. Then, count how far you've placed it.
Remeber that if you are moving to the $\to$ right it is simply in $\cdot {10}^{-} 10$ But, when moving to the $\leftarrow$ left it is $\cdot {10}^{10}$

Just note that if the power of 10 is (-) negative, it is a small quantity. However, if the power is (+) positive, of course, it is a large quantity.

May 16, 2018

$5.59 \times {10}^{-} 4$

#### Explanation:

Scientific notation is a way of writing very big or very small numbers quickly and accurately without having to use a string of zeros.

It indicates how many times a number has been multiplied or divided by $10$

It is written in the form $a \times {10}^{n}$ where $1 \le a < 10 \mathmr{and} n \in Z$

This means that the number must have one (non-zero) digit before the decimal point (it is between $1 \mathmr{and} 10$ ) and the index must be an integer.

Move the decimal point so there is one digit to the left of it.
Count the number of places it moved,

$0 \textcolor{b l u e}{.0005} 59 \rightarrow 5.59 \times {10}^{\textcolor{b l u e}{- 4}}$

You can also find this using fractions:

$0.000559 = \frac{5.59}{10000} = \frac{5.59}{10} ^ 4$

Using a law of indices this gives $5.59 \times {10}^{-} 4$