# Question #59a15

Feb 3, 2017

$4.5375 \times {10}^{1}$

#### Explanation:

$\frac{3}{8} = 0.375$

$\Rightarrow 45 \frac{3}{8} = 45.375$

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

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

Expressing 45.375 in this form means writing the number as a value between 1 and 10

$\Rightarrow 45.375 \to 4.5375$

and to get the decimal point back to where it should be means multiplying by 10

$\Rightarrow 4.5375 \times 10 = 45.375 \leftarrow \textcolor{red}{\text{ the original value}}$

$\Rightarrow 45 \frac{3}{8} = 45.375 = 4.5375 \times {10}^{1} \text{ in scientific notation}$