# How do you write the number 420000 in standard form?

Jan 13, 2017

$4.2 \times {10}^{5}$

#### Explanation:

A number expressed in $\textcolor{b l u e}{\text{standard form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{a \times {10}^{n}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where " -1<=a<10" and n is an integer}$

We have to write 420000 as a number between 1 and 10

The decimal point in 420000 is at 420000color(red)(•)

and we want 4color(red)(•)20000 so that it is a value between 1 and 10

To place the decimal point back to it's original position means moving it 5 places to the right, effectively multiplying by 100000

$\Rightarrow 4.2 \times 100000 = 4.2 \times {10}^{5} \leftarrow \text{ in standard form}$