# How do you write 13,560,000 in scientific notation?

Feb 27, 2016

$\text{ } \textcolor{b l u e}{1.356 \times {10}^{7}}$

#### Explanation:

$\textcolor{b l u e}{\text{How it works}}$

Scientific notation format is that you have a single, non zero digit to the left of a decimal point and everything else to the right of it.

The problem in doing this is that you changed the value. So you have to apply a correction that if it were to be implemented would return the number back to its original format.
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Example: Consider the value of 23

To convert this into the required format you would divide it by 10

so that $23 \div 10 = 2.3$

the problem is that $2.3 \ne 23$

However: $2.3 \times 10$ does
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$\textcolor{b r o w n}{\text{So what has happened?}}$

We have done two thing.

$\textcolor{b r o w n}{\text{Step 1}}$

We multiplied 23 by 1 but 1 was in the form of $\frac{10}{10}$

" "color(brown)( 23xx10/10" " = " "23/10xx10)
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$\textcolor{b r o w n}{\text{Step 2}}$

We applied the division but leave the other ten in place:

$\text{ } \textcolor{b r o w n}{2.3 \times 10}$
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$\textcolor{b l u e}{\text{Solving your question}}$

Given:$\text{ } 13560000.0$

Keeping the decimal place still we have to slide the digits to the right for 7 digits to get: 1.356

So we have
$\text{ } 13560000.0 \times {10}^{7} / {10}^{7}$

$\text{ } \frac{13560000.0}{10} ^ 7 \times {10}^{7}$

$\text{ } \textcolor{b l u e}{1.356 \times {10}^{7}}$