Lesson video

Hi, my name's Mr. Chan and in this lesson we're going to learn how to convert large standard form numbers into ordinary form.

Let's begin with a recap of what standard form numbers look like.

Standard form numbers begin with a number that must be greater than one, and also less than 10.

And that's multiplied by a power of 10, the index number must be positive or negative and it must be a whole number.

Here are some examples.

Five multiplied by 10 to the power of seven, 3.

9 multiplied by 10 to the power of eight, and 1.

31 multiplied by 10 to the power of negative 17.

As you can see, the format of all those fit the standard form criteria.

Here are some numbers that look like they're standard form but are not.

Negative three times 10 to the power of 12, we cannot have that because the number is not greater than one.

81.

6 multiplied by 10 to the power of 14, that doesn't quite fit the criteria of a standard form number because the beginning part of that number is greater than 10, it must be less than 10.

And finally, six times 10 to the power of 1.

5.

Again the criteria is not fit there because the index number is at 1.

5, it must be a whole number.

Here's a question for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here's the answer, hopefully you identified the correct standard form card.

With you the cards, they're not quite in standard form, let's go through them.

29 multiplied by 10 to the power of two.

The first part of that card is 29, it's greater than 10, so there's the problem.

0.

12 multiplied by 10 to the power of two.

Well, again it's the first part of that number, 0.

12, it's got to be greater than one.

3.

2 multiplied by 10 to the power 2.

5.

The problem with that number is that the index number 2.

5 is not a whole number, so that card is not standard form either.

27 multiplied by 10 to the power of two.

Very similar to the very first card, 27, that number is greater than 10, so it cannot be a standard form card.

So let's look at converting large standard form numbers to ordinary form.

Let's begin with an example.

Here we've got 7.

3 multiplied by 10 to the power of three.

Well, we know that 10 to the power of three means 10 repeatedly multiplied by itself three times.

So we can think of this question like this, 7.

3 multiplied by 10, multiplied by 10, multiplied by 10.

And from what we know about multiplying by 10, we shift the digits of 7.

3 left one space.

However we're going to do that three times.

So this diagram will help you understand that we're shifting those digits in 7.

3 three spaces to the left.

Now that creates two places above you that we need to fill in.

So we fill those in with zeros, and when we look at number that we're left with we get an answer, 7,300.

Here's a question for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here are the answers for question two.

Many of these cards look very similar, so hopefully you didn't get too confused with those.

So, remember that the powers of 10 tell you how many times the number 10 is getting repeatedly multiplied by itself.

So, for example 2.

9 multiplied by 10 to the power of four, that would be 10 multiplied by 10, multiplied by 10, multiplied by 10, effectively 10,000.

So you can think of that as 2.

9 multiplied by 10,000, so you're shifting those digits four spaces to the left to get an answer 29,000.

Hopefully you match those correctly.

So hopefully you've got the questions correct so far.

Let's have a look at another example.

We've got an example, 4.

03 multiplied by 10 to the power seven.

From what we know about 10 to the power of seven, that means 10 multiplied by itself repeatedly seven times.

So we can think about that like this.

So, we've got to think about 4.

03 getting repeatedly multiplied by 10 seven times, and that involves shifting those digits seven spaces to the left in terms of place value as such.

So, when we think about shifting those digits seven spaces, we get this answer.

Again, we might get some place values where there are gaps and we fill those in with zeros.

And when we write our final answer as an ordinary form number, we get the answer 40,300,000.

Here's a question for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here are the answers.

In part a, six multiplied by 10 to the power of four, 10 to the power of four as we've discussed is 10 repeatedly multiplied by itself four times.

Another way to think about that is 10 to the power of four is 10,000.

So six multiplied by 10,000, we get 60,000.

You'll notice one method of writing very large numbers in ordinary form, we separate groups of three zeros or groups of three digits with commas, that just makes the ordinary number easy to read.

Here are some more questions for you to try.

Pause the video to complete your task, resume the video once you're finished.

Here are the answers.

So quite often we do have to compare the size of standard form numbers, so one method is just to write them back into ordinary form which we've done there in the working out as you can see.

So five multiplied by 10 to the power of four is just 5,000.

Compare that to four multiplied by 10 to the power of five, that's 40,000 which quite obviously is more.

So Tommy is wrong with that question.

That's all for this lesson, thanks for watching.