All language subtitles for 3. Rounding--- [ FreeCourseWeb.com ] ---

Before we go too much further into the course let's quickly talk about rounding and how to avoid some

rounding errors.

We've got a combat scene here where damage is being taken damage is being dealt and you can see that

the values are being rounded.

However you may also notice the values aren't being rounded quite the way you might expect.

So we're probably already familiar with the traditional way that we round a number where say we have

a number two point seventy three for example.

And we want around that to one decimal place.

Well we look at the next number after our cutoff and we say that if that number is greater than or equal

to 5 then the number before it is increased by 1.

And if it's less than five then we just leave that number as is.

So two point seventy three would be rounded to two point seven.

Or if we were going to the nearest whole number then the seven is greater than five.

So the two point seven would round to three nice and simple.

One thing to watch out for is when the number that needs to change is a nine.

Let's take an extreme example of nine point nine nine and try rounding that to one decimal place.

Well this would cause this nine here to equal 10.

Now if we can't just put 10 in that column.

So we need to put in a zero and carry the one.

We then move over to the next number on the add that one we carried.

And that would give us 10 again.

And so in this example nine point nine nine would round to ten point zero.

It's important to note that whenever you need to give an answer to a certain level of precision in this

case one decimal place you need to keep those extra digits in there even if they are just zeros.

So in this case the answer is ten point zero not just 10.

It seems quite pedantic but it can become important in certain circumstances.

So it's worth remembering another option would be to take something called the floor of a number.

And what this essentially does is always rounds the number down to the nearest whole integer.

So regardless of what decimal places we have we essentially ignore them and round down there in our

example of two point seven three over here.

The floor would be to the opposite of this would be something called the ceiling of a number.

And what this does is always rounds the number up so again with our example of two point seven three

this would round up to three like it would normally.

But if we have another number say three point two this would round up to four and for the eagle eyed

among you you may know that that was what was actually happening in that combat clip at the start of

the video so why do we care about all of this.

Why don't we just round normally and be done with it.

Well let's say we have an enemy who is attacking our player.

This enemy is very weak compared to our player and only manages to inflict zero point six to points

of damage after some other modifiers have been added to it.

If we choose to round normally then this would do one point of damage but if it were any weaker then

it would probably do none at all or we could choose to be generous to our player and take the floor

of the number.

In essence we're saying the damage is always rounded in the player's favor.

And in this case it would do no damage at all.

Or we could do the opposite and be a little more harsh and always round the damage up by taking the

ceiling of the number an enemy would always be able to inflict some small amount of damage no matter

how weak it is in comparison to our player.

And this means that even the lowest level monster can kill our hero if they're on their absolute last

legs with all that said one thing to note at this point is that whenever you're doing a calculation

of any kind you should always perform the rounding last.

Otherwise you can start to introduce small errors and may compound over time.

For example let's take 5.1 times four point seven and then add 2.5 to that if we do that sum then it

gives us twenty six point four seven.

And if we round that then we get 26.

However if we round those numbers first say some function is returning a rounded version of the calculation

we get five times five plus three and that equals twenty eight.

And as you can see the end results are quite different.

So be very cautious when you're doing these sorts of thing to make sure these errors don't stack up

over time because this can lead to all sorts of weird and wonderful and unexpected behaviors in your

game with all of that out the way.

Let's look at how we might implement this in code.

Most modern languages have some sort of math library that you can access and the syntax is fairly similar

between each one.

So for rounding we can use math dot round.

And then in the parentheses you'd include the number you want to round and the level of precision that

you're looking for.

So this would be say 1 for one decimal place or five for five decimal places etc. the floor and the

ceiling are very similar to this except we don't need to specify any level of precision since we're

always just rounding to the nearest whole number so we have math dot floor passing in our number and

we have math dot seal passing in our number.

Notice though that the method for sealing has been abbreviated to seal here CEI L and that's usually

the case across the board.

So it's worth keeping in mind.

Okay.

So hopefully that clears up how rounding works and how to avoid some of the common pitfalls you might

come across.

We haven't covered rounding with significant figures yet but we'll cover that when we get on to scientific

notation finally.

It's time for your challenge.

So I'd like you to take the number six point two eight three and I'd like you to find the flaw of this

number.

I'd also like you'd find the ceiling of the number and I'd like you to find the number two 1 and 2 decimal

places.

So once you've got your answer pop it in the community forum and I'll see you in the next lecture.