Round 0.0078 to 1 s.f.

Using a calculator or otherwise, work out the volume of a cube with length 6.5cm. Give your answer to 3 significant figures.

Find the area of a rectangle with a base of 9.8 cm and a height of 4.8 cm. Give your answer to 3 s.f.

Round 13490 to 2 s.f.

Calculate √45 correct to 3 s.f.

Use your calculator to work out the value of:

Rounding to Significant Figures

﻿Hello, welcome to today's lesson on rounding and range with me Miss Oreyomi. You will be needing your paper and your pen or something to write on and with, pause the video now if you need to go get your equipment and make sure that there are no distractions around you and press play when you're ready to. Okay in today's lesson, you will be able to know the range of value you can take once rounded, and you'll also be able to write the range of these value to huge inequalities. What are inequalities? Inequalities are used to show the relationship between two sides. So we use the equal sign to show that the left hand side is equal to the right hand side. Inequality is used to compare both sides. So we can say for example, the left hand side is less than the right hand side, the left hand is greater than or equal to the right hand side. So we're going to be using some of these terms, some of these words in today's lesson. Your Try this task, these two students are saying two different statements. So our first student Cala is saying the population of London is 9 million and Yasmin is saying, that's 20 times bigger than Leeds. How accurate do you think Cala and Yasmin statements are? And I've put a hint there, you might want to search up London's and Leeds populations. You might want to put on a Google search and see how accurate Cala's and Yasmin's statements are. So pause the video now and attempt this task, once you finish writing how accurate you think the statements are, resume watching the video and proceed with the lesson. Okay, we're going to come back to that Try this task, but first, let's think about this number 3000. Question is what numbers when rounded to the nearest thousand would round to 3000. So, I want you to either write down on your books some numbers or shout out loud some numbers and I'm going to write some numbers that I come up with in this box as well. So I've got 2560, I've got 2987 say, I've got 3001, I've got 3499 and then if I want to be really precise, 3,499.999 recurring. Okay, we have the numbers, I've got 3218 and let's do one more 2712. So, all these numbers here, when rounded either up or down would round to 3000. Okay? How can I display this range of numbers on a number line? What is the lowest number, that would round to 3000? That would be, I'm just going to put it here 2500 and what is the highest number rounded to the nearest thousand, that would give me 3000? And that should be 3500. Now you may be thinking No, no, no, that's not right, because if I round 3500 to the nearest thousand, I am going to get 4000. Yeah, you're correct. There's a way however, to show that we mean every number from 2500, but not including 3500 and the way we do that is to shade this circle here. So we shade the circle to mean we're including the number 2500 and then we have an open circle under the number 3500. The open circle means the number 3500 is not included in our range. So that should be a straight Line. So our range of values, that when rounded to the nearest thousand would give us 3000 is between 2500 and 3500. Our number includes 2500 but it's everything up to 3500. So I could write it as this x, x means any value, any number is greater than or equal to 2500, but it is less than 3500. That any value, that is greater than or equal to 2500 would round up to 3000 to nearest thousand and any number that is less than 3500 would round down to 3000 to the nearest thousand. One of this one, what numbers when rounded To the nearest 10 would round to 70? To the nearest 10 this time. Our range should be between, we've got numbers like 68,62, oops, not 62. 65, 73, 74.8 for example, would round to 70, what else we've got 65.25, to the nearest 10 would round to 70. What else we've got 70.8. Let's do one more, we have 74.9. Okay, now we can keep on right like that, trying to write values that when rounded will round to 70 or we could express this on a number line like we did in the previous slide. So, to show the range of values, when rounded would round to 70, we know that the lowest value that would round to 70 is 65 to the nearest 10 that is, that would round to 70 is 65 and the highest value that could round to 70 is 74.99999 or we could just try 60, 75. We could write 75 here and what would we do with our circle? We wouldn't shade it in, not shading in means we're not including the number 75 and then I'm going to draw a straight line here to connect my two ranges. And how can I write that as an equality? I'm going to start with x, x means the range of values between the sets and on the left hand side I'm going to have 75 is less than, 75 but x must be greater than or equal to 65. Okay, if we go to our Try this task and our student have said the population of London is 9 million. Now we know that the exact population of London is not 9 million. When I checked on Google, it gave me an approximate number of 8.9. So we know that our student Cala has rounded to the nearest 1 million. That means our range of values would be somewhere between 8.5 million and 9.5 million, but our value would not include 9.5 million because if we round 9.5 to the nearest million, that would give us 10 million, exactly. So our range of values would be between 8.5 million and 9.5 million. That is how we write it as an equality right here. Now you're all going to get a chance to do your independent task. So I want you to pause the video now and attempt the task. Once you're done, come back and we'll go through the answers. So pause the video now, and attempt the task. Okay, so I am going to, this is the answer for one a, it's between 145 and 155. So, this means our value includes 145. So I'm going to shade 145. That's one, four, five. However, this means it doesn't include 145, so am just going to have an open circle to 155 like so, and just draw a line to join the two together. I really hope yours is neater than mine. Next one, again we're told to draw the range of values on a number line. So again, I'm going to You have 22500 here. I'm going to have 23,500 on this side, connected together. This is shaded in because it includes the number 22,500. However, this is an open circle and again I draw a straight line in between to show that these are my range of values that will be true to rounding 23,000 to the nearest thousand. Okay checking your answer for number three, for number four, number five. Why is Ade incorrect? Because if Ade rounds 350 to the nearest hundred that is 400 and that is greater than 300. So the greatest number of marbles he could have had is 349. Okay, you now have your explore task, it is wanting you to compare two values and see in which one is greater in a sense. So the Comedy theatre gets 5000 customers a day, and this has been net bounded to the nearest thousand and then the second theatre gets 5300 customers a day. However, this has been rounded to the nearest hundred and our student is asking us, does this mean the Comedy theatre gets more visitors? You think. I want you to pause the video now and think about question properly arrange the of values and decide who do you think has more visitors, the Comedy theatre or the Tragedy theatre? If you're struggling to know what to do, I'll provide some support in the next slide. So you can either pause the video and work on your own or keep watching to receive some support. For support, we have a student who is telling you to think about the range of values that when rounded to the given degrees of accuracy would give 5000 for the Comedy theatre. So what numbers if you round to the nearest thousand, would give you 5000 for the Comedy theatre or what range of values that if you round to the nearest hundred, will give you 5300 for the Tragedy theatre? So once you've find those range of values, what venue do you think would have more customers? So also to join out and see if that support is able to help you. Okay, we have now come to the end of today's lesson, a very big well done for sticking through right to the end and following the lesson. I hope you've learned lots about rounding and range and I hope to see you next lesson.

A teacher asked two students to round the number 5,469,704. Their answers are below. Which student(s) rounded the number correctly? Explain your answer.

I think about a number and rounds it to the nearest hundred. My answer is 5300. What is the greatest possible number I could have thought of?

Halima is planning a concert to raise money for charity. Entry to the concert is £5.00. The number of people attending the concert is 700 to the nearest hundred. What is the lowest possible amount of money she raised for charity?

The population of Northern Ireland is 1.9 million, to the nearest hundred thousand. What is the lowest possible number of people that live in N.Ireland?

The population of Northern Ireland is 1.9 million, to the nearest hundred thousand. What is the greatest possible number of people that live in N.Ireland?

The population of Birmingham is 1.1 million rounded to nearest hundred thousand. What is the range of values for the population of Birmingham?

Rounding and Range Quiz

In this lesson, we will learn about range when it comes to rounding numbers. We will investigate what range a number could be in based upon how it was rounded.

Maths

Y8 Maths

Key Stage 3

Year 8

Miss

Rounding and Range

Accuracy and estimation

Number

THEME

UNIT

Rounding numbers using a number line

Rounding from a calculator: Approximating

Rounding to significant figures (Part 1)

Rounding to significant figures (Part 2)

Upper and Lower Bound

Solving Problems with Rounding

Estimation

Estimate the total cost of 32 books at £178 each and 57 markers at £22.30 each.

Student A estimated that 23.5 x 91 = 1800. Student B estimated that 23.5 x 91.4= 2160. What did student B do?

Work out an estimate for 9.97% of 3967

Estimate the value of: 6.2 + 7.9 x 3.2 - 9.8

I estimated that 7.85 x 29 = 240. Why is my estimated answer more than my exact answer?

Lesson overview:Rounding and Range

Core Content

Accuracy and estimation: