Lesson video
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Hi, I'm Mr Chan.
And in this lesson, we're going to learn about converting small standard form numbers to ordinary numbers.
Let's look at how we convert small standard form numbers to ordinary farm.
We're going to begin by recapping our negative powers of 10.
So let's start with 0.
1.
0.
1 we know is equal to 1/10.
10 we can write as 10 to the power of one, so that's equal to 1/10 to the power of one.
And from our work with indices previously, we know that this is 10 to the power of negative one.
So we can think of these all being equivalent.
0.
1 equals the same as 10 to the power of negative one.
0.
01 is the same as 1/100.
A hundred we can think of as 10 to the power of two.
So we can rewrite this fraction as 1/10 to the power of two.
And this is equal to 10 to the power of negative two.
Similarly 0.
001 is equal to a thousandth, 1/1000, which is equal to 1/10 to the power three.
And that's equal to 10 to the power of negative three.
Hopefully you can see a pattern emerging, as such.
We're going to need these negative powers of 10 in order to convert small standard form numbers to ordinary form.
Here is a question for you to try.
Pause the video to complete the task, resumed the video once you're finished.
Here is the answers.
As you can see, there are many ways of writing 0.
001.
If you're unsure, have a look at the example at the beginning of this lesson.
Let's look at an example.
Seven multiplied by 10 to the power of negative three.
10 to the power of negative three is equivalent to 0.
001.
So this calculation becomes seven multiplied by 0.
001, which we can work out to equal 0.
007.
And that's our ordinary form number.
Another example.
6.
2 multiplied by 10 to the power of negative six.
So we can think of that as the same as 6.
2 multiplied by 0.
000001.
When we work that out, that would be equal to 0.
0000062.
And that would be our ordinary form number.
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 for question two.
Please be really careful when checking your answers so that you're counting the number of zeros after the decimal point really carefully.
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 for question three.
With this question, you've got to be really careful to make sure you include all of the digits in the ordinary number.
So for example, if we look at three b, we have the standard form number 3.
05 multiplied by 10 to the power of negative three.
So in our ordinary number, we must include those digits three, zero, and five.
So we get the final answer 0.
00305.
Let's look at how we compare to standard form numbers.
We've got two numbers here that look very much alike.
Five multiplied by 10 to the power of negative four, and four multiplied by 10 to the power of negative five.
So we've got to decide which one's the greatest standard form number and which one's the smallest standard form number.
So let's begin.
Five multiply by 10 to the power negative four.
We can think of as five multiplied by 0.
0001, which would equal 0.
0005.
The four multiplied by 10 to the power negative five, we can think of as four multiplied by 0.
00001, which would equal 0.
00004.
And when we compare these two standard form numbers, we're looking for which number has the bigger place value from the left hand working right.
So we can quite clearly see that the five multiply by 10 to the power negative four does have a great place value in the 10,0000ths column.
It has a five there, whereas the other number has a zero there.
So we can quite clearly say that five multiplied by 10 to the power of negative four is greater than four multiplied by 10 to the power negative five.
Here is some questions for you to try.
Pause the videos complete the task, resume the video once you're finished.
Here's the answers.
One method to compare standard form numbers is to actually write them back into ordinary form and compare them that way.
That's what I did with question five.
So to compare the densities of helium and hydrogen, I converted both of those standard form numbers into ordinary numbers, and then compared them that way.
I did find that helium has a greater density.
That's all for this lesson, thanks for watching.
