# How do you write 3324 in scientific notation?

Mar 3, 2018

The number $3324$ in scientific notation is $3.324 \cdot {10}^{3}$.

#### Explanation:

A number written in scientific notation looks like this:

$a \cdot {10}^{x}$

where $1 \le a < 10$ and $x$ is a integer.

To put $3324$ in scientific notation, first, factor out $10$ over and over until the number is between 1 and 10:

$\textcolor{w h i t e}{=} 3324$

$= 332 \textcolor{red}{.4} \cdot \textcolor{b l u e}{10}$

$= 33 \textcolor{red}{.24} \cdot \textcolor{b l u e}{10} \cdot \textcolor{b l u e}{10}$

$= 3 \textcolor{red}{.324} \cdot \textcolor{b l u e}{10} \cdot \textcolor{b l u e}{10} \cdot \textcolor{b l u e}{10}$

Now, condense all the $10$'s using the law of exponents:

$\textcolor{w h i t e}{=} 3.324 \cdot 10 \cdot 10 \cdot 10$

$= 3.324 \cdot {10}^{\textcolor{red}{1}} \cdot {10}^{\textcolor{b l u e}{1}} \cdot {10}^{\textcolor{g r e e n}{1}}$

$= 3.324 \cdot {10}^{\textcolor{red}{1} + \textcolor{b l u e}{1}} \cdot {10}^{\textcolor{g r e e n}{1}}$

$= 3.324 \cdot {10}^{\textcolor{p u r p \le}{2}} \cdot {10}^{\textcolor{g r e e n}{1}}$

$= 3.324 \cdot {10}^{\textcolor{p u r p \le}{2} + \textcolor{g r e e n}{1}}$

$= 3.324 \cdot {10}^{3}$

This is the number is in scientific notation.

Mar 3, 2018

$3.324$ x ${10}^{3}$

#### Explanation:

Most scientific notation problems require you to find the answer multiplied by 10 to a power, depending on how many units there are in the number.
Since this number has four units, it will be to the $3 r d$ power, and changed to $3.324$.

• Note: ALWAYS put the decimal place in the 'ones' position. (eg. 1.00 or 1.2345)

These answers may vary depending on how many significant figures are required, but there is no specific statement for that here, so I assume it does not apply.
That, however is another lesson entirely.