Lesson video

Hi, I'm Mr. Chan.

And in this lesson, we're going to learn how to convert small numbers to standard form.

Let's look at how we convert small numbers to standard form.

In order to do this, we need to understand negative powers of 10.

So let's recap some things we already should know.

0.

1 we should know is 1/10.

And the 10, we can write as 10 to the power of one, so we can rewrite this 1/10 as one over 10 to the power of one.

And this equals 10 to the power of negative one.

0.

01 we can write as 1/100.

And the 100, we can rewrite as 10 to the power of two.

This would equal 10 to the power of negative two.

0.

001 we can write as 1/1000, which is equal to one over 10 to the power of three.

This equals 10 to the power of negative three.

And as you can see, there's a pattern developing as such.

Have a look at this.

This will become useful in order to convert small numbers to standard form.

Here's some questions for you to try.

Pause the video to complete the task.

Resume the video once you've finished.

Here are the answers.

Hopefully from this task, you can see a pattern emerging with powers of 10.

For example, 10 to the power of three, 1,000.

We can see a one followed by three zeroes.

And when you're working with negative powers of 10, the results are a similar pattern.

Can you spot it? So let's look at some examples of writing small numbers to standard form.

Here, we're going to write 0.

007 in standard form.

So let's begin.

0.

007 we can think of as seven multiplied by 0.

001.

That would equal 0.

007.

Now, from what we've answered previously, 0.

001 is the same as 10 to the power of negative three.

So we can write this as seven multiplied by 10 to the power of negative three.

And that's asked under form number.

Let's have a look at another example.

0.

00061 in standard form, we can think of that as 6.

1 multiplied by 0.

0001.

Now that 0.

0001, we can think of as 10 to the power of negative four.

So we can complete our standard form number as 6.

1 multiplied by 10 to the power of negative four.

Here is some questions for you to try.

Pause the video to complete the task.

Resume the video once you're finished.

Here are the answers.

In question two, 10 to the power of negative three is equivalent to 0.

001, so essentially, those two calculations are the same.

And in question three, a very similar question where we're asked 0.

003 is the same as three multiplied by 10 the power of negative three.

Here's some more questions for you to try.

Pause the video to complete the task.

Resume the video once you're finished.

Here are the answers.

Standard form becomes quite tricky when we're working with very small numbers simply because you've got to be really careful counting how many zeroes there are leading up to the first non-zero number.

So hopefully, you got all those correct.

Here's another question for you to try.

Pause the video to complete the task.

Resume the video once you're finished.

Here are the answers.

So in question five, we get the answer four multiplied by 10 to the power of negative seven.

There is a nice link between how many zeroes there are between the decimal point and the first non-zero number as to what power of 10 we use.

See if you can spot it.

That's all for this lesson.

Thanks for watching.