# How do you write 1764.9 in scientific notation?

Aug 2, 2016

$1.7649 \times {10}^{3}$

#### Explanation:

The objective is to have just one non zero digit to the left of the decimal and the rest of the numbers to the right. This changes the value so a correction has to be built, shown but not applied. In this case the correction is $\left(\times {10}^{3}\right)$

$\textcolor{b r o w n}{\text{With practice you will be able to do this in a lot less lines}}$

Showing what is happening 1 stage at a time

$\textcolor{b l u e}{\text{Stage 1}}$
Multiply by 1 but in the form of $\textcolor{m a \ge n t a}{1 = \frac{10}{10}}$

$1764.9 \textcolor{m a \ge n t a}{\times \frac{10}{10}} \text{ " =" " 1764.9/(color(magenta)(10))color(magenta)( xx 10)" " =" } 176.49 \times 10$
'.................................................................................................

$\textcolor{b l u e}{\text{Stage 2}}$
Multiply by 1 but in the form of $\textcolor{m a \ge n t a}{1 = \frac{10}{10}}$

$176.49 \times 10 \textcolor{m a \ge n t a}{\times \frac{10}{10}} \text{ " =" "176.49/10xx10^2" " =" } 17.69 \times {10}^{2}$
'..............................................................................................

$\textcolor{b l u e}{\text{Stage 3}}$
Multiply by 1 but in the form of $\textcolor{m a \ge n t a}{1 = \frac{10}{10}}$

$17.649 \times {10}^{2} \textcolor{m a \ge n t a}{\times \frac{10}{10}}$

$= \frac{17.649}{10} \times {10}^{3} \text{ "=" } \textcolor{b l u e}{1.7649 \times {10}^{3}}$