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Hello, how are you today? My name is Dr.
Shorrock and I am excited to be taking you through this learning today.
This lesson is from our unit, Rounding and Solving Problems with Numbers with Up to Seven Digits.
The lesson is called "Round Seven-Digit Numbers to Any Power of 10." As we move through the learning today, we are going to deepen our understanding of rounding using a number line in stem sentences to support our rounding justifications.
By the end of this lesson, I hope that you'll be able to round any number to any power of 10.
Now, sometimes new learning can be a little bit difficult, but it's okay, because I know if we work really hard together, then we can be successful, and I'm here to guide you through the learning.
Let's get started then, shall we? How can we round seven-digit numbers to any power of 10? These are the keywords for our learning today.
We have round and critical.
It's always good practise to say these new words aloud, so let's do that together now.
My turn, round, your turn.
Nice, my turn, critical.
Your turn.
Fantastic.
When we round, we make a number simpler, but we keep its value close to what it was.
The result is less accurate, but it's easier to use.
And something that is critical, well, it has crucial importance.
Let's start our learning today by rounding to the nearest multiple of 100,000, and we have Aisha and Lucas to help us in our learning today.
Look at this number line.
What do you notice about it? Do you notice it starts at three million and ends at four million? There are 10 equal parts, so each interval must be worth 100,000, so the number line is increasing in steps of 100,000.
What can we say about the letter A? Well, we can say that A is greater than three million, but it's smaller than 3,100,000.
You can see that from its position on the number line.
We can say that A is between three million and 3,100,000.
We can say the previous multiple of 100,000 is three million and we can say that the next multiple of 100,000 is 3,100,000.
A, we can see it is nearer to three million than it is to 3,100,000.
We can say then that that A is three million when it's rounded to the nearest multiple of 100,000.
And we can show this information about a with an inequality.
Three million is less than A and A is less than 3,100,000.
and we can say that A is three million when it's rounded to the nearest multiple of 100,000.
Let's check your understanding with that so far.
Could you complete the sentences to describe the letter B? B is between mm and mm.
The previous multiple of 100,000 is mm, the next multiple of 100,000 is mm, B is nearest to mm, B is mm when rounded to the nearest multiple of 100,000.
Pause the video while you have a go at completing the sentences, and when you are ready to go through the answers, press Play.
How did you get on? Did you notice that B is positioned between 3,300,000 and 3,400,000? The previous multiple of 100,000 is 3,300,000, and the next multiple of 100,000 is 3,400,000.
B is nearest, it's closest to, isn't it, 3,400,000? So we can say that B is 3,400,000 when rounded to the nearest multiple of 100,000.
Instead of using a letter, we're now going to look at this concept with the context of a number.
Our number is 3,015,465.
What can you say about that number? Did you notice that 3,015,465 is between three million and 3,100,000? The previous multiple of 100,000 is three million and the next multiple of 100,000 is 3,100,000.
3,015,465 is nearest to three million.
We can say then that it is three million when it's rounded to the nearest multiple of 100,000.
And we can share this information with an inequality.
Three million is less than 3,015,465, which is less than 3,100,000, and that shows that 3,015,465 is three million when it's rounded to the nearest multiple of 100,000.
Let's check your understanding with that.
Could you complete the sentences to describe 3,762,001? 3,762,001 is between mm and mm, the previous multiple of 100,000 is mm, the next multiple of 100,000 is mm, 3,762,001 is nearest to mm, 3,760,001 is mm when rounded to the nearest multiple of 100,000.
Pause the video while you have a go at completing those sentences, and when you are ready to go through the answers, press Play.
How did you get on? Did you say that 3,762,001 is between 3,700,000, and 3,800,000? The previous multiple of 100,000 is 3,700,000 and the next multiple of 100,000 is 3,800,000.
3,762,001 is nearest to 3,800,000.
So we can say that 3,762,001 is 3,800,000 when it's rounded to the nearest multiple 100,000.
Lucas now uses a number line to round 5,734,000 to the nearest multiple of 100,000.
And Lucas says 5,734,000 is 700,000 when rounded to the nearest 100,000.
Do you agree with Lucas? He has made a mistake, hasn't he? What is his error? Can you spot it? Aisha is going to suggest that we use the stem sentences to help find the error.
5,734,000 is between 5,700,000 and 5,800,000.
The previous multiple of 100,000 is 5,700,000.
The next multiple of 100,000 is 5,800,000, 5,734,000 is nearest to 5,700,000, and we can say that 5,734,000 is 5,700,000 when rounded to the nearest multiple of 100,000.
Did you spot the mistake that Lucas made? His answer of 700,000 did not have the correct value, did it? It was missing that five million.
You cannot change the value of a number that drastically.
So he should have answered 5,700,000, not just 700,000.
Now have a look at this number line in these numbers.
What do you notice about them? We've got 3,379,163 and we've got 3,421,188.
Is there something that you notice about them? Well, we've noticed that 3,379,163 is smaller than 3,400,000, whereas 3,421,188 is greater than 3,400,000.
The nearest multiple of 100,000 for both numbers though is 3,400,000.
So that means that both of those numbers are 3,400,000 when rounded to the nearest multiple of 100,000.
Let's revisit these numbers.
What do you notice? So 3,015,465 rounded to the previous multiple of 100,000, which was three million, 3,762,001 rounded to the next multiple of 100,000, which was 3,800,000, 3,379,163 rounded to the next multiple of 100,000, which was 3,400,000, and 3,421,188 rounded to the previous multiple of 100,000, which was 3,400,000.
Did you notice that when we round to the nearest 100,000, the 10,000s digit is the critical digit? If it's four or less, we round to the previous multiple of 100,000 like we did for 3,015,465 and for 3,421,188.
But if the critical digit is five or more, we round to the next multiple of 100,000.
So that critical digit is really important.
It's crucial in helping us to decide how to round.
Let's check your understanding with this.
By looking at the critical 10,000s digit, determine which multiple of one hundred thousand 6,349,999 rounds to.
Complete these sentences.
The critical 10,000s digit is a mm.
This means we rounded the mm multiple of 100,000.
6,349,999 is mm when rounded to the nearest multiple of 100,000.
Pause a video while you have a go and when you're ready to go through the answers, press Play.
How did you get on? Let's have a go.
The critical 10,000s digit is a four.
This means we rounded the previous multiple of 100,000.
This means 6,349,999 is 6,300,000 when rounded to the nearest multiple of 100,000.
How did you get on with that? Well done.
It's your turn to practise now.
For question one, could you round these numbers to the nearest multiple of 100,000? You could use a number line, you could look at the critical digit and use the stem censuses to help you.
For question two, Lucas says, "The population of Kentucky is four million when rounded to the nearest multiple of one million.
The population of Oregon is 4,100,000 when rounded to the nearest multiple of 100,000.
This means that the population of Oregon must be greater than the population of Kentucky, because 4,100,000 is greater than four million." Do you agree with Lucas, and could you give reasons to support your answer? Pause the video while you have a go at both questions and when you are ready to go through the answers, press Play.
How did you get on? For question one, you had to round these numbers to the nearest multiple of 100,000.
7,510,000 while the previous multiple of 100,000 will be 7,500,000 and the next multiple of 100,000 will be 7,600,000.
That critical 10,000s digits is a one, this means we round to the previous multiple of 100,000.
So 7,510,000 is 7,500,000 when rounded to the nearest multiple of 100,000.
For part b, 5,909,810, that critical digit is a zero, so we round to the previous multiple of 100,000.
For part C, the critical digit is a five in 3,051,000, So we round to the next multiple of 100,000.
For part d, 549,999.
That critical digit is a four, so we round to the previous multiple of 100,000.
For Part d, the critical digit is a five in 450,010, so we round to the next multiple of 100,000.
609,898, that critical digit is a zero, so we round to the previous multiple of 100,000.
For question two, you had the problem to solve about the population of Kentucky being four million when rounded to the nearest multiple of one million and the population of Oregon being rounded to 4,100,000 when rounded to the nearest multiple of 100,000.
You might have said that you disagreed with Lucas and given reasons like, the population of Kentucky could be as great as 4,499,999, which would be four million when rounded to the nearest multiple of one million.
The greatest that the population of Oregon could be is 4,149,999, any greater than this and it would round to the next multiple of 100,000, which would be 4,200,000.
So the population of Kentucky must be between 3,500,000 and 4,449,999, and that of Oregon must be between 4,050,000 and 4,149,999.
So the population of Oregon could be greater than Kentucky, but it might not be.
And we can represent this as inequalities.
How did you get on with those questions? Well done.
Fantastic learning so far.
I can see how hard you are trying.
Let's move on now and look at how we can round it to any multiple of a power of 10.
The library in the town where Lucas lives has 1,756,451 books.
Did you know that we can round this number to make it simpler, to make it easier for us to read? We can round it to any power of 10.
When we round to the nearest multiple of one million, we need to consider the digit in the millions place, one, and the critical digit, which is the digit to the right, the seven.
So then we can write an inequality.
The previous multiple of one million is one million, and the next multiple of one million is two million.
The critical digit is greater than five, so we need to round to the next multiple of one million, which would be two million.
1,756,451 is two million when rounded to the nearest multiple of one million.
When we round to the nearest multiple of 100,000, we need to consider the digit in the 100,000s place, which is the seven, and the critical digit, which is the digit to the right, in this case, the five.
We can identify our previous multiple of 100,000, which is 1,700,000, and our next multiple of 100,000, which is 1,800,000.
The critical digit is a five, so we need to round to the next multiple of 100,000.
1,756,451 is 1,800,000 when rounded to the nearest multiple of 100,000.
Let's check your understanding with this.
The library in the town where Lucas lives has 1,756,451 books.
We have just together rounded to the nearest one million and rounded to the nearest 100,000.
Could you round to the nearest 10,000? Pause the video while you do that, and when you are ready to go through the answers, press Play.
How did you get on? Did you notice that the digit five is in the 10,000s place and has a value of 50,000? And we can use this to identify the previous and next multiples of 10,000, so that would be 1,750,000 and 1,760,000.
The digit to the right of the five is a six, and this is the critical digit.
Six is greater than five, so 1,756,451 is 1,760,000 when rounded to the nearest multiple of 10,000.
We can represent this as an inequality.
How did you get on with that? Well done.
Let's round 1,756,451 to nearest multiples of different powers of 10.
When we are rounding to the nearest multiple of 10, the critical digit is the ones digit.
We can see it's a one.
So 1,756,451 would round to the previous multiple of 10, which is 1,756,450.
If we round to the nearest multiple of 100, we need to look at the critical digit, which is the 10s digit, and this digit is a five, so it means we round to the next multiple of 100, which is 1,756,500.
Then we can look at the four as a critical digit if we're rounding to the nearest multiple of 1,000.
This means we would round to the previous multiple of 1,000, 1,756,000.
Then, if we want to round to the nearest multiple of 10,000, we look at the critical digit, which would be in the 1,000s place.
We would then have to round to the next multiple of 10,000, because the critical digit is a six, 1,760,000.
We can then look to rounding to the nearest multiple of 100,000.
We look at the 10,000s digit for the critical digit here, and it's a five, so that means we round to the next multiple of 100,000, 1,800,000.
Then we can look at rounding to the nearest multiple of one million.
The critical digit is in the 100,000s place, it's a seven, so we round to the next multiple of one million, which is two million.
What do you notice about all of these? Aisha noticed that the rounded numbers have at least the same number of zeros as the power of 10 which it's being rounded to.
For example, when we rounded to the nearest multiple of 10, 10 has got one zero and the rounded number has got one zero.
When we rounded the nearest multiple of 1,000, 1,000 has got three zeros and our rounded number had three zeros.
I wonder if you noticed that.
Let's check your understanding of that.
If we round 1,298,005 to the nearest multiple of 10,000, would we get a, 1,200,000, b, 1,290,000, c, 1,300,000, or d, 1,310,000? Pause the video while you have a think about this, and when you are ready to go through the answers, press Play.
How did you get on? Did you say it must be c? The digit we are rounding to has a value of 90,000, so the previous multiple of 10,000 is 1,290,000 and the next multiple is 1,300,000.
The critical digit is an eight, so we need to round to the next multiple of 10,000.
This is 1,300,000.
1,300,000 is a multiple of both 100,000 and 10,000.
How did you get on with those? Well done.
It's your turn to practise now.
For question one, a concert in aid of charity raises 289,910.
Could you imagine that you are writing a newspaper headline to report on this? Round the amount raised to the nearest 10 pound, 100 pound, 1,000 pound, 10,000 pounds and 100,000 pounds.
Then decide which figure to use in your headline.
Question two, is this true or false? And give reasons for your choice.
Part a, Aisha says that 289,910 will not change if she rounds it to the nearest 10.
Lucas says that 1,439,500 is 1,439,510 when he rounds it to the nearest 10.
Question three, Lucas is thinking of a number.
His number is 230,000 when rounded to the nearest multiple of 10,000.
When he rounds his number to the nearest multiple of 1,000, he gets the same answer.
What could his number be, and how do you know? Pause a video while you have a go at those questions, and when you are ready to go through the answers, press Play.
How did you get on? Let's have a look.
A concert in aid of charity raises 289,910 pounds.
You were asked to imagine you were writing a headline after you had rounded the amounts.
When we rounded it to the nearest 10, we got 289,910 pounds, to the nearest 100, 289,900 pounds, to the nearest multiple of 1,000, 290,000 pounds, to the nearest multiple of 10,000 was also 290,000 pounds.
300,000 pounds was rounded to the nearest multiple of 100,000.
You might have noticed that 289,910 gave the same answer when rounded to the nearest multiple of 1,000 and 10,000.
This is because 290,000 is a multiple of both 1,000 and 10,000.
You might then have chosen to use the 300,000 pounds amount in your headline to make the amount simpler to understand.
Charity concert raises about 300,000 pounds.
True or false for question two? Aisha says that 289,910 will not change if she rounds it to nearest 10, and you might have noticed that this is true.
You may have reasoned that the 289,910 is already a multiple of 10, so it will not change when rounded to the nearest multiple of 10, because it is a multiple of 10.
Part B, Lucas says that 1,439,500 is 1,439,510 when rounded to the nearest 10.
Well, you might have noticed that that is false.
You may have reasoned that 1,439,500 is already a multiple of 10, because multiples of 100 are also multiples of 10, and so it will not change when rounded to the nearest 10.
For question three, we had to figure out what Lucas's number was.
His number is 230,000 when rounded to the nearest multiple of 10, so the smallest his number could be is 225,000 and the largest is 234,999, but it also rounds to 230,000 to the nearest multiple of 1,000, which means the smallest his number could be is 229,500 and the largest is 230,499.
So his number could be anywhere in between 229,500 and 230,499 inclusive, so that means including both of those as well.
How did you get on with those? Well done.
Fantastic learning today.
I can see how hard you have really tried and your understanding of rounding seven-digit numbers to any power of 10 has really increased.
We know that when rounding, we need to identify the digit that is in the place value place that the number is being rounded to, and that helps us to determine the previous and next multiples.
We know that to identify the digit to the right of this because this is the critical digit and it tells us whether to round to the previous multiple or next multiple.
If the critical digit is a four or less, we know to round to the previous multiple, but if it is a five or more, we round to the next multiple.
Well done today.
I have had great fun learning with you and I look forward to learning with you again soon.
