# How do you express 0.000564 in scientific notation?

Feb 23, 2017

$5.64 \times {10}^{-} 4$

#### Explanation:

A number expressed in $\textcolor{b l u e}{\text{scientific notation}}$ has the form.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{a \times {10}^{n}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
$\text{where "1<=a<10" and n is an integer}$

Expressing 0.000564 in this form means writing the number as a value between 1 and 10

$\Rightarrow 0.000564 \to 5.64$

and to get the decimal point back to where it should be means moving it 4 places to the left from where it is in the 'new' form.

A move of 4 places left is achieved by multiplying by 10^(color(red)(-4)

$\Rightarrow 0.000564 = 5.64 \times {10}^{-} 4$