Lesson video

Hi, everyone, my name is Ms. Ku, and I'm really happy and excited to be learning with you today.

It's going to be a fun and interesting lesson, and some of our Oak pupils will be here to help as well.

It's gonna be tricky in parts, but don't worry, we'll all be here to help.

And I really do hope that you'll enjoy the lesson and find it challenging too.

Really excited to be working with you.

So let's make a start.

Under the unit estimation and rounding, today's lesson, we'll be looking at truncating.

And by the end of the lesson, you'll be able to estimate a value by truncating to a given degree of accuracy.

Now our key words will consist of a degree of accuracy.

So remember, a degree of accuracy shows how precise a number or measurement is.

For example, to the nearest centimetre is a degree of accuracy, to the nearest 10 is a degree of accuracy, one significant figure is a degree of accuracy, so on and so forth.

We'll also be looking at the word truncation.

And truncation is the simplifying of a number by cutting off one or more of the digits and replacing them with zeros if necessary to preserve place value.

For example, 3,678 truncated to one significant figure is 3,000, and 0.

3678 truncated to two decimal places is 0.

36.

We'll look at this more in our lesson today.

And our lesson will consist of two parts.

We'll be looking at truncation first, and then truncating in real life in the second part of our lesson.

So let's have a look at truncating first.

Truncate comes from the Latin word truncare, which means to shorten and originates from the word truncus, which means trunk.

Essentially, we are shortening a number just to give us the trunk of a number.

So imagine, it's a bit like a tree, and we're identifying where we want to cut the tree, thus leaving us with the trunk.

Let's look at some numbers.

For example, we're going to truncate 4,589 to one significant figure.

So let's have a look at our number first.

4,589, well, what is our first significant figure? I always like to use a place value chart as it helps us to remember the magnitude of our number.

So here, you can see I've put my number in our place value chart.

Let's identify our first significant figure.

Well, it's four.

So if the question wants us to truncate to one significant figure, I'm going to cut from here because this is the trunk or the digit we keep.

We're keeping the first significant figure.

Now, remember the magnitude, ensuring we keep the magnitude of the number, we simply insert the zeros.

So truncating 4,589 to one significant figure is simply 4,000.

Now Aisha says, "When I truncate 4,589 to one significant figure, I get 5,000." So can you explain why Aisha thinks that the answer is 5,000? Well, hopefully you spotted.

It's because Aisha has rounded to one significant figure, and this is completely different to truncating to one significant figure.

When truncating, you do not change any of the digits before the truncation.

Very different to rounding.

Now let's have a look at a check.

We have to truncate 59,894 to two significant figures.

Now, Jacob says, "The answer's 59." Andeep says, "The answer's 60,000." And Aisha says, "The answer is 59,000." Who is correct? And can you explain the other errors? See if you can give it a go, and press pause if you need more time.

Well done.

So let's see how you got on.

Well, hopefully you can spot Aisha's correct.

Jacob wrote the first two significant figures but lost the magnitude of the number.

And Andeep has rounded the number to two significant figures.

Aisha has correctly truncated.

Let's have a look at another check.

Here, I want you to pair the numbers with the truncated values.

We have 1,598, 2654, 24.

563, and 19.

986.

I want you to pair it with the correct statement, which states it's been truncated to one significant figure to give 10, truncated to one significant figure is 1,000, truncated to one significant figure is 2,000, and truncated to one significant figure is 20.

See if we can match these up and see if you can also explain why.

Well done.

Let's see how you got on.

Looking at 1,598, I'm going to truncate to one significant figure.

Well, while highlighting where I'm cutting off, you can see I'm going to keep my first significant figure, and everything else becomes a zero, keeping the magnitude of the number.

So therefore, 1,598 truncated to one significant figure is 1,000.

Next, 2,654.

Well, to one significant figure, that means we're keeping the two, ensuring we keep the magnitude of the number.

That means we make everything else zero.

Thus, we've changed our 2,654 and truncated it to one significant figure, giving us 2,000.

24.

563, identifying our first significant figure, we've got two.

Thus, ensuring we put in the necessary zeros, that's simply keeping our 20.

Remember our place value chart.

So 24.

563 truncated to one significant figure is simply 20.

Next, 19.

986.

Well, let's identify our first significant figure and cut off from there.

Identifying the one as the first significant figure.

Ensuring we keep the magnitude of the number changes our 19.

986 into 10, truncated to one significant figure.

Well done if you got this one right.

So when we truncate large and small numbers, the process is still the same, and it's important to pay attention to the degree of accuracy.

For example, if the question want us to truncate 0.

027815 to two significant figures, what do you think the answer would be? Well, let's identify that second significant figure first.

Hopefully you can spot it's the seven.

Remember, significant figures use the first non-zero digit.

From here, we're going to identify or cutoff point.

Remember this is the trunk or the digits that we keep.

Everything else becomes a zero where necessary.

So ensuring that we keep the magnitude of the number, we simply insert zeros where necessary.

Here, I didn't have to put my zeros in because 0.

027 preserves the magnitude of the number.

Using this, let's have a look at another check.

Three pupils were given this calculation.

Were asked to truncate 12.

235 to two decimal places.

Who do you think is correct and explain the error the other students have made.

See if you can give it a go.

Press pause if you need more time.

Well, let's see how you got on.

Jacob says, "Is it 12.

23?" Andeep says, "Is it 12?" And Jun says, "Is it 12.

24?" Well, hopefully you've spotted Jacob is correct.

Let's look at this.

Jacob truncated the number to two decimal places.

Andeep rounded the number to two significant figures.

And Jun has rounded it to two decimal places.

Well done if you got this one right.

Well done.

So let's move on to another check.

Do you think you can truncate these numbers to two significant figures? And I also want you to truncate these numbers to two decimal places.

See if can give it a go, and press pause if you need.

Well done.

So this question is a great question as it really does deepen your understanding of those degrees of accuracy.

So let's have a look at truncating to two significant figures first.

Well, on the first question, we notice that the six of the 5682.

6234 is our second significant figure.

So truncating, we should simply have 5,600.

Now truncating to two decimal places, you might notice it's the two.

So therefore, truncating to two decimal places, we have 5682.

62.

0.

86252, truncating to two significant figures focuses our attention on that six.

Thus, our answer is 0.

86.

To two decimal places, well, we're still looking at that six again.

So the answer is 0.

86.

Moving on to 682.

9956.

Our second significant figure is eight, so therefore, we simply have 680.

Our second decimal place is our nine.

So truncating, we have 282.

99.

Truncating 0.

000125 to two significant figures means we're looking at the two.

So that's our cutoff.

So we have 0.

00012.

And truncating to two decimal places, well, this is really nice as we've identified our second decimal place to be zero.

So our answer is 0.

00.

Well done if you got any of those right.

Great work, everybody.

So let's have a look at your task.

Here, you need to complete the table.

You're truncating to one significant figure, two significant figures, or one decimal place.

See if can give it a go.

Press pause if you need more time.

Well done.

Let's move on to question two.

Question two is a wonderful cross number puzzle.

See if you can give this a go, and press pause if you need more time.

Fantastic work, everybody.

So let's have a look at question three.

Question three is a number detective, and you need to work out the number given the clues.

So part A states, "I am what? Truncated to one significant figure, I am 200.

I'm a multiple of 12.

I am 250 when rounded to the nearest 25.

I am a palindrome." In other words, the number reads the same as if if all the digits were reversed.

Part B says, "What am I? When truncated to one significant figure, I'm 100.

I'm also a multiple of four.

I am 200 when rounded to the nearest 100.

And the sum of my digits is 15." This is a great question, see if you can find out what those numbers are.

Well done, let's move on to these answers.

Well, for question one, let's see how you got on.

Here are our answers when truncated to one significant figure, two significant figure, and one decimal place.

Well done.

For question two, let's see how you got on here.

Here are our numbers when you've truncated these values to the degree of accuracy stated, or if you rounded the numbers to the stated degree of accuracy.

Great work if you got this one.

Next, question three.

These are our two answers, 252 and 168.

These were really tough, so well done if you've got any one of these.

Great work, everybody.

So let's have a look at the second part of our lesson, looking at T truncating in real life.

Now, truncating can be used in lots of different ways.

For example, how could you use truncating to estimate the answer to 813 multiplied by 11.

8? Well, you could truncate 813 to one significant figure, giving us 800.

You could truncate 11.

8 to one significant figure, giving us 10.

Thus, our estimate calculation would be 800 multiplied by 10, which is 8,000.

But Laura states that it works well for this calculation.

What about 898 multiplied by 18.

7? Well, how could we truncate to estimate the answer to 898 multiplied by 18.

7? Well, we could truncate 898 to one significant figure, giving us 800.

We could truncate 18.

9 to one significant figure, giving us 10.

That means we get 800 multiplied by 10, which is 8,000, which is our estimate to the calculation.

But Laura has made a really good point.

She says, "The estimate for 898 multiplied by 18.

7 is the same as the estimate for 813 multiplied by 11.

8." Laura is correct.

And truncation is a method of approximating numbers, and it might be quicker than rounding, but it does not always give the best approximation to the original number or an estimate to the calculation.

Now, Laura says she doesn't like truncating.

And she says, "It seems unreliable and pointless, and rounding is much better." Alex says, "Truncating is very useful in everyday life.

You probably don't realise that we truncate often." Laura says, "Can you give me some more examples please?" A really nice example is when Laura went to the cinema to see a film rated 12.

Now it doesn't matter if Laura was 11.

99 years old or 11 1/2 years old, didn't make a difference at all.

You are not allowed to see the film as you are still classed as 11 years of age.

Even if it was one day before your 12th birthday, you are still classed as 11 years old.

Laura wants another example.

Well, let's have a look at where Laura had 129 pounds and wanted to buy as many five-pound candles as possible.

How do you think Laura would've calculated how many candles she could have bought? Well, she did 129 divided by 5, which is 25.

8, so that means she could only buy 25 candles.

Alex explains that this is a really good example of truncation.

She truncated her answer as she only wants the integer value.

This was a really nice way to show how we use truncation in real life.

Let's have a look at a check question.

In computer science, INT capitals or in lowercase is used to truncate a number so to only give the integers.

For example, if you were asked for the integer of 56 divided by 10, you'd have an output of 5.

This is because 56 divided by 10 is 5.

6, and the programme truncates this, and it only wants to focus on the integer value.

So the integer of 5.

6 is simply 5.

That's why the output is 5.

Now what I want you to do is have a look at what do you think the output would be if the syntax was INT(123/10)? If the syntax was INT(5.

23/2)? Or if the syntax was INT(48/31)? What do you think the outputs would be? Well done.

Let's see how you got on.

Well, the output for the first one would be 12.

This is because 123 divided by 10 is 12.

3.

Truncating this only to give us integers is 12.

B wants us to work out the integer value of 5.

23 divided by 2.

Well, the output would've been 2.

This is simply because 5.

23 divided by 2 is 2.

615, we're truncating into your values, so that means the output is 2.

For part C, we need to work out the integer value 48 divided by 31, which is simply 1.

Well done if you got this one right.

The context of the question determines whether it's suitable to truncate an answer, round an answer, or use the exact value of an answer.

Read the question carefully and think about what the value of the answer means will help identify if you need to work out a truncated answer, round answer, or work out the exact value of an answer.

So let's have a look at a check.

Here, we have three scenarios which require the calculation 75 by 3.

When should you calculate the exact answer? When should you truncate the answer? Or when should you round the answer? See if you can have a look at these context and determine what do you think you need to do.

Press pause if you need more time.

Well, let's have a look.

Seven pizzas shared between three people.

Well, this definitely needs an exact value because we want to make sure everyone gets a fair share.

In other words, if you were to do 7 divided by 3, that means everybody gets 2 1/3 of a pizza each.

Aisha has seven pounds and wants to buy as many three-pound chocolate bars as she possibly can.

Well, this is where we truncate the answer because 7 divided by 3 is 2 1/3.

And she can't buy 1/3 of a chocolate bar, so we truncate because she can only afford an integer number of chocolate bars.

Let's have a look at the last one.

A bill of seven pounds is shared between three people.

This is where we round because money's in two decimal places.

We want to make sure that we pay enough.

This means each person should pay 2.

33 pound, maybe one person pays one pence more, but we needed to round because 7 divided by 3 was 2.

3 recurring, and we had to round because money is given to two decimal places.

Well done if you got this one right.

Great work, everybody.

So now it's time for your task.

Question one says, "Given the scenarios below, identify if the answer should be given exactly, rounded, or truncated." See if you can give it a go, and press pause If you need more time.

Well done.

Let's move on to question two.

Question two shows a broken calculator screen.

And the question asks, "What is the largest and smallest number that could be displayed on the screen?" See if you can give it a go, and press pause if you need more time.

Great work.

Let's have a look at question three.

Question three, we're looking at that computer science example again.

Remember INT, uppercase or lower cases, used to truncate a number, so to only give the integers.

Remember that example, INT(56/10) will give us an output of 5 because 56 divided by 10 is 5.

6, and we only want the integer.

So we truncate to give the 5.

See if we can work out A, B, and C.

Great work, everybody.

Let's move on to question four.

Question four states, "Lucas is going on holiday and looks at the exchange rates.

One pound is equal to 1.

16887 euros.

Now, travel firms and banks offer a truncated value of this.

In other words, one pound is equal to 1.

16 euros.

Why do you think truncating exchange rates are better for travel firms and banks? And also, if 1 million pounds exchanged, how much money would the travel companies and banks make due to truncation?" This is a great question, see if you can give it a go.

Well done.

Let's go through these answers.

Well, for question one, Aisha is 14.

7 years of age and wants to see a 15 rated film.

Can she go? Well, no, unfortunately.

The truncated age is 14 years of age, so she's below age.

Next, a bookshop has 89 pounds and wants to buy as many 1.

99 pound puzzle books as possible.

How many books can it buy? Well, we truncate here too because the bookshop can only afford integer number of books.

Lastly, a bill of 89 pounds is shared between 10 people.

It's best to round because money is two decimal places, and this means each person should pay 8.

90 pound, or pay nine pound each, leaving a little tiny tip.

Well done if you got this one right.

Question two, what's the largest and smallest number that could be displayed on the screen? Well, given the numbers concealed, we can see the truncated value.

The largest value is 1.

299999 going on, and the smallest value is simply 1.

2.

For questions three, let's see how you got on.

Well, INT(45/8) gives an output of 5.

Here, you have to work out what the output was.

Well, we should have had an output of 9, add an output of 2, thus, giving us a total of 11.

The next one, well, working out those individual outputs, it should be 16, add 6, subtract 1, giving goes a total output, 21.

Great work if you got this one right.

For question four, well, question four is a really nice question because banks and travel firms truncate exchange rates.

So let's find out why they do this.

In this case, for every one pound exchanged, the bank or travel company actually gain 0.

00887 euros.

So what does that mean if we had 1 million pounds exchanged? Well, if we multiply that 0.

0087 by 1 million, this means banks and travel firms, in this case, gain 8,870 euros per million pounds exchanged.

So this is all due to truncation.

Great work if you got this one right.

Fantastic, everybody.

Well done.

You can see that we can truncate large and small numbers, and the process is still the same, but it is really important to pay attention to the degree of accuracy.

Remember, truncation is a method of approximating numbers and it's easier than rounding, but doesn't always give us the best approximation to the original number or an estimate to a calculation.

The context of the question determines whether it's suitable to truncate an answer, round an answer, or use the exact value of an answer.

Great work today, everybody.

It was tough in parts.

You did so well.