Lesson video

Hello, my name's Miss Parnham.

In this lesson, we will be rounding with up to three significant figures.

Before we round to significant figures, let's determine what they actually are.

Significant figures are the most powerful digits in the number, the first digit in the number which is not zero.

So, for 243, it is the two representing 200, in 4,105, it is the four representing 4,000, in 23.

64, it is the two representing 20 and in 0.

967, it is the nine representing nine tenths, not the zero, the zero is simply a placeholder.

And in 0.

0601, it is the six representing six hundredths, which is the most significant figure.

Let's it's round 4,217 to one significant figure.

The most significant figure of this number is four representing 4,000, so this number lays between 4,000 and 5,000.

So, when we round this to one significant figure, it is as if we are rounding to the nearest thousand.

Now, 4,217 is about here and we can see, it's a lot nearer 4,000 than 5,000, so to one significant figure, 4,217 approximates to 4,000.

Let's now identify the second significant figure, before we round to two significant figures.

So, in 243, that is four representing four tens, in 4,105, it is one representing 100, in 23.

64, it is three representing three ones, in 0.

967, it is six representing six hundredths, in 0.

0601, it is in actual fact the zero, even though I said that zeros could not be significant, if we've already started to count significant numbers, so the six is the first significant number, then any zeros that subsequently follow that are now counted as significant figures.

Let's round 4,217 to two significant figures.

We can see that the second significant figure here is two representing two hundreds, so this is akin to round into the nearest hundred.

So, let's think about 4,200 and 4,300 because this number lies between those two.

It's about here, so 4,217 rounds to 4,200 to two significant figures.

Let's now identify the third significant figure in these numbers.

It should be obvious for 243, it is three, 4,105, it is the zero, in the 10th position, this is because we have already started counting significant figures before this and in this instance, this zero can be considered as a significant figure.

In 23.

64, six in the tens position is the third significant figure and in 0.

967, seven is the third significant figure, following six, which is the second significant figure and nine, which is the first significant figure.

And then 0.

0601, one is the third significant figure.

Let's round 4,217 to three significant figures.

The third significant figure in this number is one, the one tens, so this is going to be akin to round into the nearest 10.

So, this number lies between 4,210 and 4,220, somewhere about here, therefore, 4,217 is rounded to 4,220 to three significant figures.

Here are some questions for you to try, pause the video to complete the task and restart the video when you're finished.

Here are the answers.

Notice that rounding to significant figures is particularly useful for very small numbers, such as 0.

00593 in part d, if we'd have rounded that to two decimal places, then we'd have got 0.

00, which tells us absolutely nothing about that number.

Here are some questions for you to try, pause the video to complete the task and restart the video when you're finished.

Here are the answers.

It may have been tempting with part a and part e because they were quite large numbers, to round to a more accuracy than three significant figures, but if that's what we're asked to round to, then we must stick to that and use zeroes in the place of numbers to keep the correct place value.

Here are some questions for you to try, pause the video to complete the task and restart the video when you've finished.

Here are the answers.

52,400, when rounded to three significant figures, is the same as rounding to the nearest hundred because the third significant figure represents hundreds in that number.

So, when we were looking for the highest number of people, we think about the halfway point between 52,400 and 52,500 and that's 52,450, but that number would round up, so just subtracting one from that, gives us the highest number of people that could have been at the match.

And then for the lowest number, we're thinking about the halfway point between 52,400 and 52,300, which is 52,350 and that's where that number, of the lowest number of people that could have been at that match, comes from.

Here are some questions for you to try, pause the video to complete the task and restart the video when you're finished.

Here are the answers.

So, here we had to work out the area of a triangle, so that would be multiplying 0.

456 and 0.

306 together and dividing by two and then we round the answer.

The second shape we have there is a square, as indicated by the lines showing that those sides are all equal in length and we can see right angles there in that shape.

So, we're either going to multiply 4.

305 by itself, or use that squared key and then round our answer to three significant figures.

That's all for this lesson, thank you for watching.