## Video-Lesson Transcript

In this lesson, you will learn how to write numbers in scientific notation.

The basic form of scientific notation is

Whereas can be any integer and can be positive or negative.

Whereas is

Or can also be negative

Whereas is constant.

Here’s an example:

It’s really

Let’s say we have

It’s really

and then

If we have

it could be written as

which really is

See , , and are our . All of them meet the requirement above.

Likewise, all the exponents are integers.

Here’s an example of a negative exponent.

This is

which is

To review our lesson in Exponents, we have to change the sign to move the denominator to the numerator.

So since we want to move the denominator to the numerator, we have to write

This is a bit tedious work.

Don’t worry. There’s a quicker way to do this!

## Writing Scientific Notation by Counting Decimal Places

For example, we have

Let’s get where then multiplied by

So it’s

Then let’s count the decimal spaces from the right of and stop to get .

We counted decimal spaces.

This goes right in as our exponent.

So now we have

Let’s have another one.

Remember, we need to have a number that is less than so we can’t have .

Instead, we can have

So, we’ll have

Then let’s count how many decimal spaces are there in for us to get

There are decimal spaces. This goes right in as our exponent.

We counted from the right to left. Meaning it’s a big number and we’re making it small.

Now, we have

Now, let’s have a small number.

Let’s get a number between and .

That is

Multiplied by which is constant

Then let’s count the decimal spaces to have the value of our exponent.

We counted decimal spaces.

So we’ll have

But remember we counted from left to right. Which means it’s a small number and we’re making it big number.

We have to counteract that by making the value of our exponent negative.

So our final answer is

Exponent should be in negative if we have a small number and we’re writing it to appear a big number.

On the other hand, an exponent is positive if our original number is big and we’re writing it to become a small number.

Let’s have one more example.

We have

The number between and is

Our exponent is since we moved three decimal spaces to get .

Moreover, it should be in negative because we have a small number.

So the scientific notation is

Another way to look at the value of exponent:

If you moved the decimal to the left, you’ll have a positive exponent.

And if you moved the decimal to the right, you’ll have a negative exponent.

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