Multiplying and dividing in standard form

Key Stage 3

Maths

Indices and standard form

Write the following number in standard form: 700

Write the following number in standard form: 45587000

Write the following number in standard form: 708900

Write this as an ordinary number: 3.0450 x 10^4

Write this number as an ordinary number: 6.5 x 10^6

﻿Hello, and welcome in this lesson on multiply and dividing in standard form with me, Miss Oreyomi. For today's lesson, you will be be needing a paper and a pen or something you could write on and with. Just a reminder you that you would help. If you put your phone on silence to avoid distraction, and also try to get into a space with less noise. Also, during this lesson, if you need to pause the video at any time, do so and also pause it when I tell you to, just so you can attempt the task, and you could understand what is going on in the lesson. If you want to rewind at any point. Feel free to do so, so now pause the video. If you need to go get your equipment, or get into a space with less noise and press play, when you're ready to begin the lesson. Okay, for you to try this task, you are to think about the numbers you have in your screen now, and write what is the same or what is different about the following numbers. So take a moment, pause the video, have a think about it and then press resume when you're ready to carry on. Okay, hopefully you saw that a similarity, something the same is that this three times into, to five has been written out here as an ordinary number. So this number is as standard form. This number is an ordinary is written as an ordinary number, but they're essentially the same thing. So 300,000 is the same as saying three times into the five. And the same for this five times ten into three, is been written out here. Did you also notice how, this five times into the three, is written here and it's multiplied by this three times into the power of five. Perhaps something different you thought was that, we have swapped the powers for this here. So instead of having three times into the five, we've had 500 times into, the three into the three, and here we've got five times into five. Did you manage to work out this calculation? And what was your answer? Hopefully you noticed that, regardless of whether we do this or this or this or this calculation, our on size always 15 times, 10 to the eight, and we are going to be seeing through this lesson. How, what happens when we multiply in standard form and what happens when we divide in standard form? So take our first example, three times into the power of five, multiply by five times into the power of three, so I took the Liberty of actually writing this out as an ordinary number, and then carrying out the calculation. Let's count the number of zeros we have when we do this calculation out, so I've got one, two, three, four, five, six, seven, eight, Okay, so here, I could say, my answer is 15 times, 10 to the power of eight. But we're in standard form. Would this be my final answer in standard form? Not quiet, because we said this first part of our number, must be a number between, it must be a number between one and 10. So here I must have, I must have a number that is between one and 10. And at the moment 15 is not between one and 10. Have you noticed, or do you know a way I can make 15 to be a number between one and 10? I could divide by 10, right? If I divide 15 by 10, what am I left with? 1.5, now, because I have divided 15 by 10. What must I do to my power of 10 to make it equal, That would give me the same answers what I started with. Hopefully you said that because I divided by 10, I must increase my power by 10 as well. So 1.5 times 10 to the power of nine is the same as 15 times 10 to the power of eight. Except now, our number here is in standard form. Standard form. So, what you need to think about is, my first part of my number, this part here, must be a number between one and 10. Haven't done that though, do you notice something when we're multiplying in standard form? Well, I just multiplied my base, didn't I? three times five is? 15 and then what did I do with my powers? I added them, so I've got my base three times five 15, and then I added my powers five plus three is eight, hence that eight over there. So when I'm multiplying in standard form, I have to multiply my base together and at my powers, let's try another example there. I've got three times into the power four multiply by two times into the power of six, instead of doing it out, working it out like this, what could I do? Well I know that I could multiply my base together. Three times two is? Six isn't it? And then if I'm adding my powers, four plus six is? 10, so it was going to be 10 times, 10 times six times 10 to the power of 10. Now, do I need to do anything to my final answer here? Well, no, I don't do I, because six is between one and 10. So I just leave it like that, three times into the power of four, multiplied by two times into the power six. In standard form my answer is, six times into the power of 10. What if we have a negative number in our power? So I've got seven times three is, 21. Now I've got 10 to the power six, and then I've got 10 to power of negative seven. What am I doing with my powers? I am adding them, so over here, if I put it in bracket six, and then I'm adding a negative seven, what's that answer going to be? Well, I am adding a negative number to my, to my starting point, so I'm going to have a negative one. That's not how you write it, Is it? I'm going to have a times 10 to the power of negative one. Is this the way it's meant to be? Well, no, because 21 is greater than, 10. So looking back our first example, what must I do with 21? I must divide it by 10, so that's going to be 2.1, right? I have divided by 10, so I must increase my power by? Right, and if I increase my power by 10, I am left with? Times ten to the zero. So 2.1 times 10 to the zero is essentially the same thing as saying, 21 times 10 to the minus one. What happens when I'm dividing then? When I'm divided in standard form, what do you think happens? Hopefully your brain is thinking if I multiply, I do the inverse when I'm dividing, but let's see it. Let's see it worked out. So I've got eight times 10 to the power five, divided by four times into the power three. So as previously, I took the liberty of writing this out in as an ordinary number. So I've got 800,000 divided by 4,000 well, I could cancel out three zero's cause they're the same. And then I've got four, eight, I've got 800 divided by four. So that's going to be 200, isn't it. How can I write 200 in standard form? Hopefully you said it's two times 10 squared cause 10 squared is a hundred, so two times a hundred is 200. Instead of doing out this long way, have you noticed a way of doing this by just working with this number? Working in standard form, as opposed to writing it out as an ordinary number? Well, eight divided by four, is two. And if I am dividing in standard form, I, subtract the powers when I multiply and I added the powers when I'm dividing, I subtract the powers, so five takeaway three is, two. So I've got eight divided by four is, two. And then I subtract my power times 10 squared. Let's try another example then. I have 1.6, Times ten to the power of nine divided by four times 10 squared. 1.6 divided by four is? 0.4, isn't it? What am I doing with my powers now? Subtracting them. Nine Takeaway two is, seven. So it's going to be, times ten to the power of seven. What would that be my final answer. Not quite cause 0.4 is not a number between one and 10. So therefore, how can I get 0.4 to be a number between one and 10? I multiply by 10, so if I'm multiply 0.4 by 10, I am getting, four. I need to adjust my power though, because I have changed my first part of my number. I must adjust my power because I increased the first part of my number by 10, I must, decrease my power by 10. So I am going to be left with 10 to the power of six. So again, zero point four times ten to the seven is the same as four times ten to the power of six. Let's do one more example. I've got 12 time ten to the power of six, divided by three times ten to the negative three. So again, I am going to divide my base. 12 divided by three is, four. And over here I've got six and then I'm taking away. I'm subtracting negative three. So it's going to be times 10 to the power of nine. How about you have a go now, pause the video, have a go of this four questions and then resume the video and we'll go over the answers together. Remember to give your answer in standard form. So pause the video now, attempt this questions and press resume when you're ready to go over the answers together. Okay, how did you get on with those then? For the first one, we're doing 1.6 times 1.2 rather times five, so you should have gotten, six. And because I am multiplying in standard form, I am simply adding my powers together. So is six times 10 to the power of nine. What of this one then, I've got 1.2, Times ten to the seven divided by two times ten to the six, 1.2 divided by two is, 0.9 because, I'm divided, I have subtracted my powers. So that's going to be times 10 to the one, I'm I done? Not quite, this is not between a one and 10. So I'm going to multiply this by 10. So this is going to be nine, and then I'm going to divide. I'm going to decrease my power by 10. So this is going to be 10 to the zero, or it's just going to be nine. Next one, then multiplying again, six times three is 18, 10 to the power of negative six and then ten to the power of negative three. So that is essentially the same as say negative six adding negative three. So my final answer is going to be times 10 to the negative nine, but I need to do something to my 18. I'm going to divide by 10 to get it to be a number between one and 10, so it was going to be one point eight. Because I divided by 10, I'm going to increase my power by 10. So it's going to be times 10 to the negative eight. Last one then, nine divided by three is three, and then I'm subtracting my powers. I've got eight subtract negative two. So I've got times 10 to the power of 10. It is now time for your independent task. I want you to pause the video now and attempt every question on your worksheet, and then when you are ready, press play, and we'll go for the answers together. So pause your video now, and attempt the questions on your sheet. Okay, I hope you are able to attempt all your questions and let's go for the answers together. So two times three is six times 10 to the seven. Here we have a 30 times 10 to the eight, which is essentially the same as three times 10 to the nine. Here we have 14 times negative seven plus three. So it's be 10 to the negative four, which is again the same as 1.4 times 10 to the negative three, for D it's going to be 20 times 10 to the power of 20, which is the same as two times 10 to the power of 21. Over here, we would have 9.6, I believe times 10 to the power of five. And over here we would have 16 times. We've got negative six and we're adding negative four. So it's going to be times 10 to the negative 10. We're going get our answer between a number between one and 10, so there's going to be 1.6 times 10 to the negative nine. Okay, let's go for number two then. I've got five times times into the power of four divided by five times 10 squared. So five divided by five is one and then times 10 to the power of two. Because I'm subtracting my powers over here. I have 2.5 again, times 10 to the power of two over here. I have 0.3 times 10 to the negative 11. I am going to increase, I'm going to multiply my first part by 10 to get three. And then I'm going to decrease my power. And it's going to be times 10 to the negative 12. Over here, One divided by four is 0.25 10 to the power of 10, take away ten to the power of nine is going to be 10 to the power of one. I'm going to multiply this by 10. So it's going to be 2.5 and I'm going to decrease my power by 10, so it's going to be 10 to the zero, which is the same as one. last one, 6.2 divided by 3.1. I have two and then subtract my powers times 10 to the five doing well? Okay, let's look at question three. I have, A is four times to the five and B is 3000 and I am trying to work out B divided by A, it would help if I convert my ordinary number to standard form, so I've got three times 10 to the power of three. And i am dividing that by four times 10 to the power of five. While I know that three times three divided by four is 0.75, and then I'm going to be subtracting my powers. So that's going to be times 10 to the negative two. I am going to times this by 10 to give me 7.5, a number between one and 10, so if therefore I am going to be decreasing my power. So that is going to take me to negative three. Okay, next one then. I have C squared, so I know that my C is six times 10 to the negative two. And I'm squaring that, I'm time sing in that, by itself, six times 10 to the negative two, six times six is 36 negative two. And I'm adding negative two, that takes me to negative four. I want 36 to be a number between, I want my first part to be a number between one and 10, so I'm going to divide this by 10, so that's going to be 3.6. And then I'm going to be increasing my power by one. So it's going to be times 10 to the negative three. Okay, let's think about your explore task then. There was a headline in the newspaper, every day 12% of British people eat at Fishin restaurants. Decide whether this headline is true using the following information. There are about five times 10 to the power of three Fishin restaurants in the UK. Each restaurant serves about 2.5 times ten to the power of three people every day. And there are about seven times, seven times ten to the power of, seven Britons. So pause your video now attempt this is it true? Is the headline true or false? If you need a bit more support, then carry on watching the video. And I provide you with a little hint as I think you should be able to do this yourself, so if you're feeling confident, go for it, pause the video and attempt it. If not carry on watching the video. Okay, we're trying to see if this information is true. There are about five times ten to the power three Fishin' restaurants in the UK. Well, we've just learned about multiplying, haven't we? Multiply in standard form. What do we have here? I've got number of Fisher restaurants in the UK, and the amount of people that restaurants serve each day. So what should I be doing with both with this two information I've been given? And once I found that out, there about seven times into the power of seven Britons, what should I be doing, after I've gotten this information? What should I be doing with this information? And then how can I turn it into a percentage? Pause your video now, attempt this task. And then once you're done, carry on watching the video. We can go for the answers together. Okay, so there are about five times into the power, of three Fishin restaurants in the UK, and each restaurant serves about 2.5 times ten to the power of three people. So that tells me that I have to multiply these two numbers together. Well, I know for multiplier that what, I just have two multiply by base together don't I? So that's going to give me 12 point five. So I've got 12.5 here, times 10 to the power of six. Now I know this is not in standard form, so there's going to be 1.25, times 10 to the power of seven. And there are about seven times 10 to the power of seven Britons, so I'm going to divide that by seven times 10 to the power of seven, I get an answer, of 1.25 times ten power seven divided by seven times into the power of seven. It's going to be between zero. So I get an answer of 0.1785, but I want to turn that into a percentage, don't I? So I'm going to multiply that decimal number by a hundred. So I'm going to get answer of 17.9%. So the headline is false more pigeons, eat at Fishin restaurants. Now what the headline proposedly said. We've now reached the end of today's lesson. I had a lot of fun teaching this lesson, and I hope you had a lot of fun learning as well before you go, do you complete your quiz as it would help you to know what you've learned from today's lesson, and also to remember, to complete the quiz before you go, and a very big well done for getting through the end, and I will see you on the next lesson, bye.

Multiplying and dividing in standard form

Multiplying and dividing in standard form

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UnitMaths / Indices and standard form

Maths