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Scientific Notation (Including Multiplication & Division)

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Video-Lesson Transcript

Let’s multiply and divide numbers written in scientific notation.

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

Scientific Notation 2

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