## Examples of Operations with Scientific Notation

### Example 1 $(9\times 10^4) \times (6 \times 10^8)$

First, let’s break it down to $(9) \times (10^4) \times (6) \times (10^8)$

Next, group the like terms then multiply $(9) \times (6) \times (10^4) \times (10^8)$

We’ll have $54 \times 10^{12}$

Remember, it should be greater than or equal to $1$ and less than $10$.

So let’s simplify it further by moving one decimal space to the left.

We now have $5.4 \times 10^{13}$

### Example 2 $\dfrac{36 \times 10^9}{6 \times 10^5}$

Let’s divide the like terms $36 \div 6$ is $6$ $10^9 \div 10^5$ is $10^4$

So our answer is $6 \times 10^4$

## Video-Lesson Transcript

Let’s multiply and divide numbers written in scientific notation. After you finish this lesson, view all of our Pre-Algebra lessons and practice problems.

Now, let’s move on to multiplying numbers written in scientific notation.

Here’s an example $(5 \times 10^3) \times (3 \times 10^2)$

Everything here should be multiplied

Let’s break it down to $(5) \times (10^3) \times (3) \times (10^2)$

Let’s group the like terms first then multiply $(5) \times (3) \times (10^3) \times (10^2)$

We’ll have $(15) \times (10^5)$ $15 \times 10^5$ may look like a scientific notation but it’s not.

Remember, $a$ should be greater than or equal to $1$ and less than $10$.

So let’s simplify it further by moving one decimal space to the left.

We now have $1.5 \times 10^6$ Let’s have two more examples. $(3.2 \times 10^4) \times (2 \times 10^7)$

Let’s multiply now $3.2 \times 2$ is $6.4$

then $10^4 \times 10^7$ is $10^11$

So now we have $6.4 \times 10^11$

We don’t have to make any adjustment because it is already in scientific notation form.

Let’s try this one $(5 \times 10^2) \times (9 \times 10^5)$ $5 \times 9$ is $45$ $10^2 \times 10^5$ is $10^7$

So we have $45 \times 10^7$

Then let’s move the decimal to get a value between $1$ and $10$.

The answer is $4.5 \times 10^8$

Now, let’s do division of numbers written in scientific notation.

For example: $\dfrac{8 \times 10^5}{2 \times 10^2}$

Let’s divide the like terms $8 \div 2$ is $4$ $10^5 \div 10^2$ is $10^3$

So our answer is $4 \times 10^3$

Let’s have a more difficult one $\dfrac{3 \times 10^8}{6 \times 10^4}$

Let’s do this $3 \div 6$ is $0.5$ $10^8 \div 10^4$ is $10^4$

We have $0.5 \times 10^4$

But this is not a scientific notation.

To write it down, we have to move the decimal space.

The final answer should be $5 \times 10^3$