Multiplying and dividing in Standard Form Quiz

﻿Hello, and welcome to this lesson on addition and subtraction in standard form with me, Miss Oreyomi. For today's lesson, you'll be needing your paper and your pen, or something you could write on and with. If you can get into a space with less noise and distraction, then please do so. It would also help if you put your phone on silent, so that you're not easily distracted. If you feel at any point during this lesson, that you will benefit from pausing the video, rewinding, watching stuff again, then by all means do so. Also, when I tell you to pause the video and go for a task, it would really help your understanding if you do pause the video and attempt the task. So now, pause the video if you need to get your equipment or get into a space with lesser noise, and press Play when you're ready to resume with the video. Okay, you have to try this task. You have six numbers on your screen, you're to write each of these numbers as an ordinary number, and then add them together, and rewrite them in standard form. What do you notice when you do this? So pause your video now, attempt this, and then press Resume when you're ready to carry on with the lesson. Okay, hopefully you manage to do that, if we convert this for example to standard form, it's going to be the same as 20. And if I add a number like 50,000 to 20, I'm going to get 50,020. So hopefully you notice that when you're adding, in standard form, it's the same as adding four plus two, for example. 400 plus 956, because, that leads into what we're doing in today's lesson. When we're adding in... When we add in standard form, there are no set rules, for example, where we're multiplying, we multiply the base then we add the powers, however, when we're adding in standard form, we have to convert it to ordinary numbers and then, add them together, and then convert it back to standard form. So let's try this example on our screen. I have, eight times 10 to the power of three, which is the same as eight times a thousand, so that's 8,000 here. And then I have four times 10 to the power four, which is the same as 40,000. So I am adding this together. So I've got 40,000, add 8,000, so that's zero, zero, zero, eight and four. So, this however is not in standard form, cause I've been told, to give my answer in standard form. Say, if I want to give my answer in standard form, I am going to write 4.8 times 10 to the power four. I'm going to do just one more step here before I get to standard form, so I could write this as 48 times 10 to the power of three, can't I? Because I've got three zeroes representing a thousand. However, to go from 48 to a number, between one and 10, I divide my 48 by 10, I get 4.8. And because I've divided my 48 by 10, I have to increase my power by 10, so... That's hence, why I've got times 10 to the power four. So my final answer here, is going to be 4.8 times 10 to the power of four. Let's do another example. We're going to do this, here. So, this time, I am adding, seven times 10 to the negative three, to 2.5 times 10 to the negative five. I am going to convert, seven times negative three, to an ordinary number. So I've got, 0.007. And then I'm going to convert 2.5 times 10 to the negative five, to an ordinary number, so that will be, 0.000025, and I'm going to put my place-holders there, just to help me with my addition. So here, I've got five, I've got two, I've got zero, I've got seven. I've got zero, zero point zero. This is my answer, as an ordinary number. Can I convert this to standard form? Of course I can. How can I convert, because this is essentially the same as writing 0.007025 times 10 to the of power of zero. Because 10 of the power zero is essentially one. So, how can I go from 0.007, to get a number between one and 10? Well, if I multiply this number by a 1,000, I'm going to have, 7.025, ain't I? And because I'm multiplied by a 1000, I am going to have to take my power, I take it down by a 1000, ain't I? So it's going to be times 10 to the negative three. So my final answer here, is going to be, 7.025 times 10 to the negative three. I am going to rub out the working out on that side, for this last example here. So I'm going to rub this out. So over here we have 8.4, times 10 to the three, adding 2.15 times 10 to the five. So I've got... So 2.1 times 10 to power of five is the same as writing 210,000, and then I'm adding that to... My apologies. I'm adding that to that 8,400, because if I am timesing 8.4 times a 1000, I get 8,400. So I'm going to add this together then. So that would be zero, zero four, eight, one, and two. So my answer is going to be 218,400. Again, I could write this as 218,400, times 10 to the power of zero, because that's essentially the same thing as timesing by one. Right, but I don't want this, because this is not a standard form. So I am going to divide my answer by one, two, three, four, five. So I'm going to have, 2.184, times what? What do I need to multiply... Because I divided by a 100,000, I am going to have to increase my power by, how many zeros in a 100,000? By five, isn't it? So this is essentially the same as, times 10 to the power of five. Okay, let's move on to subtraction then. Subtraction, is essentially the same as addition, except I am subtracting the original... Ordinary numbers, my apologies. So I've got 17 times 10 to the power four, which is essentially the same as 170,000. And from that I'm taking away 500. So I've got a zero takeaway zero is zero. I've got zero there. Now, I have to borrow numbers to be able to subtract this. So this is I'm going to borrow from here, I'm left of six. I'm going to borrow from here, I'm left with nine. So here 10 take away with five, is five, nine, six, and one. Convert this to standard form, again, I could write a 169,500, times 10 to the power of zero. Because I'm divided by one, two, three, four, five, to get to a number between one and 10. So here I'm going to do 1.695, because I have divided by a 100,000, isn't it? So again, I am going to have to increase this number by a hundred thousand, so that would be, times 10 to the power of five. Now I'm going to do this below here. Yeah, let's do it somewhere here. I have eight times 10 to the negative four. So that is essentially the same as writing 0.0008, and from that, I am taking away, four times 10 to the negative five, so that will be 0.00005. And I'm going to put my zero there, as a place-holder. I am going to borrow one from this eight, to be able to do my subtraction. So I'm going to be left with five, seven, zero, zero, zero, zero, point zero. Again, I want to write this in standard form, to go from 0.00075, to a number between one and 10. Well, I'm going to multiply by one, two, three, four, I'm going to multiply by 10,000. So I'm going to multiply this number by 10,000, and I have 7.5. Because I have multiplied by 10,000, I am going to decrease my power by 10,000, which is essentially 10 to the power four. So I am going to decrease my power by 10 to power four. So it's going to be, 10 to the negative four. Because remember I'm starting with 10 to the zero. So I'm decreasing it by four, so I've got 10 to negative four. Your turn then. Pause the video, attempt this three questions. If you need to rewind, to go over what I have said, then please do so, and resume watching the video, when you've had a go at these questions. Okay, let us do number one. I've got 60,000 and I am adding 800, so I've got 60,800. In standard form, I would have 6.08, times, 10, to the power of four. Okay? Because, this is essentially the same as writing times 10 to the zero, I am dividing by 10,000, to get to a number between one and 10. So therefore I am increasing my power, by 10 to the power four. Because 10 to the power four, is the same as, 10,000. Next one then, here I have, 0.0134, subtract that from 0.00621. I'm going to put my zero there as place-holders, I am going to borrow one from here. I'm left with nine, one, borrow one from here, I have a seven, zero, zero, point that. As usual, I am starting with this. I am going to multiply my number by one, two, three, four, by again, 10,000, so I've got 7.19 times... Because I multiplied my power by 10 to the power four, I am... My power... This is going to decrease by 10 to power four as well. So, to the negative four. Let's do the last one. Over here I have, 0.001. And I'm taking that away from 0.0007. Put my zero again as place-holder, borrow one from here, I have three, zero, zero, zero, point zero. Again, I want this in standard form. I am going to multiply by again 10,000. So it was going to be three... Because I multiplied it by 10,000. I am going to decrease my power by 10 to the power of four, so that is going to be, times three times... Three times 10 to the negative four. It is now time for your Independent task, so do you pause the video and attempt every question on your Independent task. I am going to go through certain answers when you press resume, to carry on with the lesson. So pause the video now and attempt your Independent task, and press Play, when you're ready to go over the lesson. Okay, how did you get on with your task? You have your answers on your screen for question one. So checking your work and marking it. You may need to pause the video if you have it marked it. And I move on with the slide. Okay, for the second one, the number of visitors to some tourist attraction is shown in the table were below. And it's asking you how many more people visited the Highland Park, than the Grace-hope-Love-Tree-House. It's asking you to subtract those two values from each other, and if you do so, your answer in standard form is going to be 7.14042, times 10 to the power of six. And this is how I went about to arrange, my numbers, so that I could subtract them. For number three, it's asking you for the total annual production for the product. Okay, so I have already arranged my numbers from the largest to smallest because I want to add them together. So I've got zero, zero, zero, zero, zero, one. So that's going to be three, 12 and, 18. And here I've got, 10, and 17, and over here, I've got 18, and four. So in standard form, my answer is going to be, 4.878, times 10 to the power of eight. Okay? How did you get on with those? I hope you found them straightforward, challenging as well, and well done for completing your Independent task. Okay, you have your Explore task. Using each of the digits, zero to nine only once. How close to 1 million can you get using this. So you're using the digit between zero to nine, and you can only use each digit ones. Where can you put your digits so that, you can get a number as close to 1 million? So pause the video now, and attempt this task. I am not going to providing any support, cause I want you to have... I want you to explore this as far as you can, without me giving you any hint. And I trust... I really trust that you can actually do this. So pause the video now, and attempt this task, and then once you're ready, press Play to carry on with the lesson. Excellent, a very big well done on getting to the end of today's lesson. So well done on completing your task, and for sticking all the way through. Don't forget to complete the quiz before you go, and I will see you at the next lesson, bye.

Addition and subtraction in Standard form Quiz

In this lesson, we will learn to add and subtract numbers written in standard form, giving your answer as both ordinary numbers and in standard form.

Maths

Y9 Maths

Key Stage 3

Year 9

Miss

Addition and Subtraction in standard form

Indices and standard form

Number

THEME

UNIT

Indices and Radicals

Indices and power of 0

Expressing powers of in different bases

Laws of indices

Fractional Indices (Part 1)

Fractional Indices (Part 2)

Negative indices

Powers of 10

Sorting large numbers

Multiplying and dividing in standard form

Mixed problems with standard form

Simplify fully  √𝟕2

Jack and Jill are arguing about surds. Jack says: √4 x √12 = √48. Jill says: √4 x √12 = 3√4. Who is correct?

Lesson overview:Addition and Subtraction in standard form

Core Content

Indices and standard form: