##Scientific notation
A number is written in scientific notation when there is a number greater than or equal to $1$ but less than $10$ multiplied by a power of $10$.
The following numbers are written in scientific notation:
- $5.4\times 10^3$
- $8.013\times10^{-6}$
Want to learn more about scientific notation? Check out this video.
##Writing numbers in scientific notation
###Numbers greater than $10$
If we have a number greater than $10$, we move the decimal point to the left until we have a number between $1$ and $10$. Then, we count the number of times we moved the decimal and write that as an exponent over a base of $10$. Finally, we write our number multiplied by the power of $10$.
Example
Let's write $604{,}000$ in scientific notation.
If we move the decimal left once, we get $60{,}400.0$. We need to keep moving the decimal until we get a number between $1$ and $10$.
We have to move the decimal left a total of $\goldE5$ times.
Now, we have $6.04$.
Finally, we multiply $6.04$ times $10^\goldE5$:
$604{,}000$ in scientific notation is $6.04\times10^\goldE5$.
###Numbers less than $1$
If we have a number less than $1$, we move the decimal point to the right until we have a number between $1$ and $10$. Then, we count the number of times we moved the decimal and write that as a negative exponent over a base of $10$. Finally, we write our number multiplied by the power of $10$.
Example
Let's write $0.0058$ in scientific notation.
If we move the decimal right $\greenD3$ times, we get a number between $1$ and $10$.
Now, we have $5.8$.
Finally, we write $5.8$ times $10^{\greenD{-3}}$:
$0.0058$ in scientific notation is $5.8\times 10^{\greenD{-3}}$.
##Practice
[[☃ graded-group-set 1]]
Want to try more problems like this? Check out this exercise.