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Hello, and welcome to this lesson on "Powers of 10" with me, Miss Oreyomi.
For today's lesson, you will be needing a paper and a pen or something you can write on and with.
It would also help if you can minimise distraction by putting your phone on silent and trying to get into a space with less noise.
If you need, if you need to do those things now, please do so; you can pause the video, and when you're ready, press play to resume the lesson.
Right, for your Try This task, you are to fill in the missing box with the calculation that will take you from this square to the circle.
So, for the first one, what would I do to go from 10 to 100? So you have to fill in that box.
So I could say, "I times by 10." So that would be your first example.
So, do the rest for B, C, D, E, and F, and then once you're done press play to continue with the lesson.
Okay, hopefully you had a go of that.
So, to go from 10 to 100, I multiply by 10.
To go from 200 to two, well, hopefully you've wrote that I divide by 100.
To go from 3000 to three, hopefully you've wrote that I divide by 1000.
To go from 0.
04 to 40, I have to multiply by 1000.
To go from 0.
5 to 0.
005 I have to divide by 100.
And then to go from 0.
006 to 60, I have to multiply by 10,000.
Hopefully this gives you a nice introduction to what today's lesson is going to be about.
So, take for example, I've got 10 squared.
I want to write it out.
How many 10s do I multiply together if I've got 10 squared? I multiply 10 by itself two times, don't I? So here I'm going to write 10 times 10, which is 100.
Okay, what if I've got 10 cubed? What does that mean? Well, I multiply 10 by itself three times.
So I've got 10 times 10 times, I'm just going to rub this out, just so I make everything aligned, times 10.
Okay? What if I do 10 to the four? Well, we're getting the hint now, isn't it? It is 10 times 10 times 10 times 10.
Now this is 100, this is 1000, this is 10,000.
Can you see what's happening each time? I am multiplying by 10 each time.
What if I've got 10 to the power of one? That's just going to be 10.
We know this from our previous lesson.
Okay, what if I've got then 10 to the minus one? So I'm multiplying by 10 each time when I'm adding my power.
If I'm going down, if I'm going, okay, let's do 10 to the zero.
10 to the zero is one, okay.
If I'm now going to 10 to the minus one, what would I do each time, then, if I'm subtracting my powers? I'm going to divide, wouldn't I? So I've got one over 10 and in index, we know one over 10 is 0.
1, okay; let's do one more.
10 to the minus two.
Well, 10 squared is 100, so 10 to the negative two would be one over 100, which is the same as 0.
01.
Hopefully, writing it like this would help us when we're working with powers of 10.
Okay, so I've got a question like seven time 10 squared.
Well, I know that 10 squared is the same as 100.
So seven times 100 is 700.
I want to use my place value grid, my place value table, to work out 52 times 10 cubed.
Well, I know that 52 and 10 cubed is 1000, so I've got my 10s, this should say ones, and I've got two ones, okay? When I'm multiplying by, when I'm multiplying by 10, 100, 1000, I move my digits three times to the value, so if I'm multiplying by 10, I move my digit once to the left.
If I'm multiplying by 100, I move my digit twice to the left; if I'm multiplying by 1000, I move my digits three times to the left.
I realise now that you're left is this way, so I move my digits three times to the left, this way, so if I move it, if I'm multiplying 52 by 1000, I am going to be moving it to the left.
So it's going to be one, moving it once, two, and three, so my five is going to end up here, and then moving my two three time again, one, two, three, so my two is going to end up here.
And I am going to write my place holders.
I'm going to put zero as my place holders just to fill in those gaps.
So my answer is going to be 52,000.
Let's try with 5.
62 times 10 to the power of three.
Well, I've got 5.
62, and again, 10 to the power of three is 1000, so I've got five, 5.
62, and I'm multiplying by 1000, so I'm going to be moving each of my digits three times to the left so one, two, three, that's going to be here.
My six is going to go one, two three, it's going to go in the six.
And my two is going to end up here.
And I'm going to put my zero here as place holders.
I can fill in the rest, but 5620.
00 is the same as 5,620.
Let us, then, I'm going to rub these out, let us try 7.
65 times 10 to the power of negative two.
7.
65 times 10 to the negative two is the same as one over 100, isn't it? So essentially, this is the same as 7.
65 divided by 100.
7.
65 divided by 100.
If I am dividing by 100, my digits, or my place value, are therefore moving twice to the right, isn't it? So, it's going to be one, two, so seven will be here.
Six would go over here, and five, one, two, would be in my ten-thousandths.
Remember what I said about place holders, I'm going to put a zero here to hold that place, my decimal point, and then a zero here again to hold that place.
So my final answer is going to be 0.
0765.
You may have realised there's another quicker way of doing this.
So for example, if I am multiplying, I'm just going to come up over here.
I've got 5.
62 times 1000.
I want to move my digits three times to the left.
So it's going to be moving it once, moving it twice, and then I'm going to move it one more time; you will see there's an empty space here.
So I'm going to fill that space with a zero.
So that gives me an answer of 5.
6, sorry, 5,620, rather.
Okay, your turn.
Out of, I've put, a decimal place value chart here for you to help you should you need it.
If I've got 8.
72 times 10 squared, and then the rest of the questions, so pause your video now.
Attempt all four questions, and then once you're done, resume and we'll go for the answers together.
Okay, hopefully you had a go at that.
If we just go for the answers very quickly, so I've got 8.
72 times 10 squared.
If I do the quick method, I've got 8.
72 times 100, so I'm going to move my digits twice to the left, so it's going to be one, two, one two, so it's going to be 872.
Let's show you that very quickly with this one.
We've got 8.
72, moving all my digits twice to the left.
My eight is going to go to my 100s.
My seven is going to go to my 10s, and my two is going to go to my ones, okay? For this one, well again, if I've got 2.
1 times, 2.
1 times 1000, I'm moving all my digits once two, three times to the left, rather, so it's going to be one, two, three.
These empty spots here means I am filling them with zero, so it's going to be 2,100, and hopefully, you're using your chart to help you, as well, as that could be a visual way of seeing it, so very quickly, I'm just going to do that example.
I've got two, 2.
1, moving all my digits three times to the left, so I've got one, two, three, two, and then my ones, one, two three, goes to the 100, and I put my zero, zero as place holders.
For the third one, hopefully, you saw that multiplying 5.
23 times 10 to the negative three is also the same as dividing by 1000 with my final answer being 0.
00523, and then for this one, it's the same as dividing by 100 so I've got, I'm moving all my digits twice to the left so it's going to be one, two, so my answer is 0.
0352.
Let's show the last one very quickly on our chart.
So, I've got 3.
52.
I'm moving all my digits twice to the right, so it's going to be one, two.
My two is going to go there.
My five is going to go there.
My three is going to go in my 100s, and I'm filling the rest with place holders, so it's 0.
0352.
Okay, so we've seen multiplication and briefly division like that.
Let's look at division in more detail then.
So I've got 32, 3,200 divided by 100.
Now there are different ways of doing this.
One way is to write it like this, and cancel out the zero.
What am I left with? 32.
If we put it on our chart, let's see if it's the same.
This is ones, not units.
So I've got 3,000, two 100s.
I am moving all my digits twice, 'cause it's 100, to the right, so moving it, moving my zeros twice to the right, I've got one, two.
That goes there; the other zero goes to the tenths.
I've got my decimal point.
My two goes to my ones, and my three, moving it twice to the right goes to my 10s.
32.
00 is the same as 32.
So again, for this one, divided by 1000, cancel out my zeros.
I'm left with 1,240, so that's my answer here: 1,240.
Right, for this, I've got 5.
23 divided by 10,000.
If I use my chart to help me, if you found a way of doing this your way, by the way, without using the chart, that is 100 percent okay.
In fact, it is encouraged to not use the chart.
The chart is just for you to see what's happening when we're moving our values either to the left or to the right.
So I've got 5.
23 and I'm moving it four times to the right, so I've got one, two, three, four, so my three is going to go there.
My two is going to go there.
My five is going to go here.
And then I've got zero, zero, zero point zero.
So my final answer here is going to be 0.
000523.
Next, I have 0.
045 divided by 10 squared is 100.
Can you tell me what's going to happen here? What do you think should be my answer? So I'm going to be doing it on my chart whilst you're doing it as well.
I've got 0.
045.
I am going to be moving all my digits to the right twice, isn't it, so that's going to be five, four, zero, zero, zero, point, zero.
Right, your turn then.
If I divide 0.
5 by 10 to the one, what would I get? And for the second one, what do I need to divide this by to get 87? And for the third one, what would be my final answer.
So pause the video now.
Attempt all three questions, and then we'll go for the answers together.
Okay, I wonder how you got on? Did you manage to answer all those questions? For the first one, is the same as dividing by 10, so it's going to be 0.
085.
I need to divide this by 10 to the three to get 87 and for this one, I am going to get 40,000.
Did you get those? Right, it is now time for your Independent task.
I want you to pause the video now.
Attempt all the questions on the, on your screen, and then press play to go over the answers.
So pause your video now to go, to work for your Independent task.
Okay, welcome back.
I hope the task was interesting and challenging and engaging; I have put the answers up for number one, so go over that and see how you got on with that, so that should be a zero.
So checking that you've gotten that.
Can pause your screen if you want to go over it in more detail.
Okay, for number two, "A coffee shop sells cups of coffee in 0.
6 litre cups.
"In one day, they sell 10,000 cups of coffee.
"How many litres of coffee do they sell?" This question is essentially asking us to do 0.
6 times 10 to the four and your answer should be 6,000 litres of coffee.
"A rectangle has an area of 821.
040 centimetres square.
"The width of the rectangle is 100 centimetre.
"What is the length?" Essentially, again, you are dividing this number by 100.
So, if I am dividing by 100, my length would be 8.
21040 centimetre because if I times, if I multiply 100 by 8.
21040 centimetre, I would get this as my area.
Okay, let's look at number four then.
We've got 25 divided by 10 squared, which is essentially the same as 25 divided by 100, which is 0.
25 and then I've got 0.
0025 times 10 to the minus one, which is essentially the same as 0.
0025 divided by 10 which is 0.
00025.
And then, lastly, 0.
25 times 100, because 100, 10 squared, is 100, so and that is 25, so the greatest is 0.
25 times 10 squared.
Greatest.
Okay? Okay, for your Explore task, you have to try and get the number 82,813.
5 using standard form.
So I have given you a very skeletal way of doing it using the powers of 10 so that I've started with eight times 10 to the power of four, add that number to two times 10 to the power of three, and I've given you one, two, three, four, four empty, four other brackets that you have to fill.
You don't have to do it this way.
If you find a shorter method, a shorter way of getting 82,813.
5 using your powers of 10 in standard form, then go for it.
So pause your video now, and attempt this using trial and error, it doesn't matter; use your calculator to help you, as well, should you wish, and then resume the video and there should be an answer on your screen when you resume the video.
So pause the video now; so attempt this Explore task.
Okay, here are two ways you could have gone about getting the number 82,813.
5.
How did you get on? Did you manage to get one of the ways? Or was your way different to what is on the screen right now? Okay, we've now reached the end of the lesson of "Powers of 10." I hope you were able to learn something new regarding the powers of 10, and even if this was more like a recap for you, complete the quiz, show yourself what you know, and also just let, let yourself know what you know by doing the quiz.
So do complete the quiz before you leave today.
And I will see you at the next lesson; good-bye.
