# How do you write 0.00083 in scientific notation?

Feb 27, 2016

With practice you will probably be able do it all in your head!
$8.3 \times {10}^{- 4}$

#### Explanation:

$\textcolor{b l u e}{\text{Explaining the principle behind this}}$

Explained by example:

Consider $2.5$

If we multiply this value by 1 we have: $2.5 \times 1 = 2.5$

The really cool thing is that you can use this principle to change the way some value looks without changing its inherent value at all:

$\textcolor{b r o w n}{\text{If you have "10/10" this this is the equivalent of 1}}$

So, if I multiply $2.5$ by 1 but the 1 is in the form of $\frac{10}{10}$ then we have:

$\text{ } 2.5 \times \frac{10}{10}$

This is the same as$\text{ } \frac{2.5 \times 10}{10} = \frac{25}{10} = 25 \times {10}^{- 1}$
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$\textcolor{b l u e}{\text{Solving your question}}$

Given:$\text{ } 0.00083$

Multiply by $\frac{10}{10}$ giving $\text{ } \frac{0.00083 \times 10}{10} = \textcolor{red}{\frac{0.0083}{10}}$

$\textcolor{b r o w n}{\text{Process repeat number 1}}$

$\text{ } \textcolor{red}{\frac{0.0083}{10}} \times \frac{10}{10} = \frac{0.0083 \times 10}{10 \times 10} = \textcolor{g r e e n}{\frac{0.083}{{10}^{2}}}$

$\textcolor{b r o w n}{\text{Process repeat number 2}}$

$\text{ } \textcolor{g r e e n}{\frac{0.083}{{10}^{2}}} \times \frac{10}{10} = \frac{0.083 \times 10}{{10}^{2} \times 10} = \textcolor{m a \ge n t a}{\frac{0.83}{{10}^{3}}}$

$\textcolor{b r o w n}{\text{Process repeat number 3}}$

$\text{ } \textcolor{m a \ge n t a}{\frac{0.83}{{10}^{3}}} \times \frac{10}{10} = \frac{0.83 \times 10}{{10}^{3} \times 10} = \frac{8.3}{{10}^{4}}$

$\textcolor{w h i t e}{.}$

" "color(green)("Write this as: " 8.3xx10^(-4))

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This is the equivalent of keeping the decimal place where it is and sliding the number to the left four places. You than apply a correction. In this case the correction is ${10}^{- 4}$ which would change 8.3 back to 0.00083 if applied.

$\textcolor{g r e e n}{\text{You have not changed the value but you have changed the way it looks!}}$