# Scientific notation review

CCSS Math: 8.EE.A.3

Review the basics of scientific notation and try some practice problems.

## 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 $\goldD5$ times.

Now, we have $6.04$.

Finally, we multiply $6.04$ times $10^\goldD5$:

$604{,}000$ in scientific notation is $6.04\times10^\goldD5$.

### 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 $5.8\times 10^{\greenD{-3}}$.