Oh, excited to be here.

Cool.

High.

So I'm Megan.

I am a software engineer.

It jack sta in city on.

I'm here today to talk to you all about numbers in general, but also specifically in javascript.

Um, and to have a little bit of fun with it.

I'm gonna put it in the context of Beyonce a little bit.

I see who here is a fan of Beyonce can actually see any of you.

So I'm just gonna assume your old fans of Beyonce and you're gonna love this talk, so I hope you all ready to learn.

So let's get back to basics.

What actually is a number?

Well, a number is an abstract concept which we use to count, measure, label and identify things.

Um, we kind of use them every day.

Um, they're pretty familiar concept, Um, And to help us kind of group them in and understand them, we can classify them, so, uh, we can group them into certain categories so we can start off with a natural numbers, which are our positive whole numbers.

Indigents.

Um, we have indigenous, which is negative and positive whole numbers and includes era.

We have rational numbers, which numbers that can be expressed as fractions, irrational numbers and numbers which cannot be expressed his fractions, such as pie or the square root of two on.

We also have real numbers.

Real numbers are a super set of all of the above categories, Um, and basically represent any number that you can see on the number line.

Um, we also have complex numbers, transcendental numbers, imaginary infinity and negative infinity infinite testicles.

It's real.

None of which I know anything about.

So not gonna go there.

So just as we can, um, classify numbers and group them into different ways, we can also represent them in different ways.

So when I talk about representation, I just mean how we communicate the numbers that way.

Using, um so inhuman languages.

If I asked you to think of the number eight, uh, many people here would imagine the Arabic numeral eight.

Um, some of us might, uh, imagine Bob, the Mandarin Chinese character.

Some of us might may think of thought, which is the Hindi, um, number eight.

So all of these are actually the same thing, that just different symbols, which we use to represent the number eight, um, And apologies.

If I've just, like, butchered the pronunciation of those feel free to come and correct me afterwards.

Eso justus We can represent numbers in different ways in human languages.

We can also represent them in different ways in jobs group.

So in Java script, there are five ways that we can represent numbers.

Um, we have outstanding based 10.

So if we imagine that number 1,234,000 567 we can also represent that as a binary number, which is based to Octel, which is based eight Hexi Decimal, which is based 16.

You use that a lot if you're working with CSS as well on dhe scientific notations.

So that little So this is what we use when we're handling really large numbers.

Um, and that a just means, like times 10 to the power off six in this case.

So what is a number in job script?

Well, just as a girl has to have has standards, so too does a programming language.

Ah, And in javascript, we follow the I e 754 um, standard for floating point arithmetic.

That's the Institute of Electrical and Electronic Engineers.

Um, it's a soup along really dry document.

If you're having trouble sleeping, I can recommend it.

Um, so it's very interesting of I just don't have the, uh, the ability to read that kind of document, but palette to you if you do.

Um, but basically, it outlines how numbers are implemented in JavaScript, um, and gives us a reason why Zahra 0.1 plus 0.2 does not equal 0.3, which is everyone's favorite JavaScript joke.

Um, so the aii 75 full specifies the implementation of floating point arithmetic in Java script, which is how we represent decimal points in boundary and that allows us to represent real numbers as an approximation to support a trade off between range and precision.

So when I talk about range and precision, computers have limited space, they're not that amazing.

Um, sorry.

No events.

Um, so when I talk about range in javascript, we have a range of numbers that's like the size of the set that we can represent, so we can represent from about negative nine quadrillion all the way up to positive nine quadrillions.

That's a pretty decent sample size.

And when I talk about precision, I main in JavaScript.

We can represent numbers safely to 17 decimal places.

Beyond that, it'll just get kind of wacky.

Um, and because computers have limited space, we have to make a trade off between range and precision.

We can either have greater range or greater precision.

We can't really have both, Unfortunately, so computers are super basic, a pun based space to you guys.

Um, this says hello.

Singable in battery.

Um, So regardless of how you write your number, everything in the your computer is gonna be stored in binary.

It's all just ones and zeros.

But we can't have decimal points in binary decimal coming from the wood deco meaning 10 um, finery is based to, So we can't really represent decimal point safely.

So a floating point arithmetic tries to account for that.

So let's think about our number one million, 234,567 underneath.

That is the representation of that number in binary floating point.

We have 64 bits, So 64 individual digits.

Um, and it's helpful to kind of think about this in terms of scientific notation if you're already familiar with it to break down these bits.

So the first bid represents the sign.

Um, if it's zero, it's a positive number.

If it's a one, it's a negative number.

The next 11 bits represent the exponent.

So how far along the decimal place should be?

Um, in this case, it would be like six points along six places alone.

Um, and we also have the significant or Mantis, um, which actually represents the the, um, like, actual digits of the number.

So let's have a look closer.

Look at everybody's favorite JavaScript bug.

Um, when I was a kid, one of my maths teachers always used to tell me that, um, calculate is never wrong.

Humans are.

Yeah, It's all I have to say about that, Mr Edwards.

Huh?

Um, So when we, uh, representing numbers in floating point arithmetic, we can represent images Super easy.

It's fine.

The conversion to boundaries.

Totally easy.

Um, but when we start representing fractions, things become a little more difficult.

So if we were trying to represents a 1/10 in finery finery is based to so representing one out of 10 in a system that only counts up to two is gonna present some complications.

Let's think about 1/3 when we represent 1/3 in decimal.

We we round it.

We don't say.

Point 33333333333333333 For the rest of our lives, we just say, 0.0.3 your 0.33 Um, but has anyone who's tried toe like implement a three column layout?

Grid layout and CSS will know it's ready 33% times three dozen equal 100%.

Always that pesky little 1%.

Um, so Al 0.1 plus 0.2 Problem is similar to this.

If we think about 0.1 represented in decimal, it's easy.

0.1.

Let's convert that to boundary.

Okay, that's a lot more complicated.

Um, I did say that we don't have decimal points in binary.

That's not a decimal point.

It's a ratings point.

A ratings finery point.

Um, so it's a similar concept, but just in base, too.

Um, we're not gonna get into that, but if you look at this representation, you'll see it.

0.0 There 110011001100 And that repetition just keeps on going.

Um, but because we only have 64 bits, we only have a certain amount of space to store this number.

We have to round it at some point.

And so when we take that rounded binary representation of their appoint one and convert it back to decimal, we got this.

So that's not 0.1.

Hence this problem.

So it's a rounding arrow.

How big a problem is this really?

If I was trying to measure one San Tomato and I had 0.16 0 hours full centimeters of era, that would be 0.903 times as long as a glucose molecule.

Okay, that seems pretty tiny.

Let's go bigger.

If I were trying to measure a kilometer and I had a margin of error a 0.16 04 kilometers, that would be 0.21 0 times as long as the distance from Earth to the moon.

Okay, No, big enough.

Let's go big or go home.

If I were trying to measure a let you, that's the distance that light travels in a year, and I had a margin of zero margin of error of 0.16 0 Full light is I'd be about 38.38 centimeters off, or about the height of a standard bowling pin.

Things you lent.

So in most cases, this degree of accuracy is really just not gonna be that important.

Um, we don't usually need to know the value to 17 decimal places.

Um, if we're creating a shopping cart, for instance, does your user really need to know they caught total to 17 decimal places?

No, I need to know what's like to maximum so we can just round it on.

And we can just round it really easily, using the grounding methods inside of the maths object.

So we've talked a bit about precision.

Now let's move on to range.

Size really does metal.

In my defense, Charlie started the willy jokes yesterday, so I'm just carrying on from her work.

So I ventured that we have a trade off between range and precision.

Um, and when I mentioned our range, I said, we have a ranging javascript of about negative nine quadrillion through two positive nine quadrillion, but I wasn't telling the entire truth.

Way to build trust.

Cool.

Um, so if I went into my job script console and I typed in 1.7 times 10 to the power of 308 I'd get that number back.

So obviously I can represent that number that's way bigger than nine quadrillion nine quadrillions only, like, 16 zeros.

And this has 308.

That's massive.

Um, but if I go 1.8 to the power times 10 to the power of 308 an infinity, I'm confused.

They're really remember that being her maths works, but okay, so job script actually has a maximum value.

Um, and you can access that inside of the number object and its 1.79769 we'll arrest those numbers times 10 to the power of 308.

So that's a really big number.

Um, And for really big numbers, we have naming conventions.

So, um, like a 1,000,000 billion quadrillion um, and there's naming conventions go all the way up to a number that is followed by 303 zeros, which is called a cent.

Ilyin.

It's a job script actually exceeds naming conventions like That's massive.

That's huge.

That's a pretty good range, if you're still not convinced that that's a good range.

Um, 3.28 times 10 to the power of 80 is the number of particles in the universe.

So if you're using any numbers bigger than that, what are you doing?

Stop.

We're gonna create a black hole or something.

Um, but if you are using numbers bigger than that, like, tell me I want to know what you're doing for real.

That's cool.

Um, so we have no business using numbers greater than that.

Maximum number.

Um, this is this is fine.

So we have a massive range up to 308 0 hours.

Um, but we can't safely represent numbers beyond this nine quadrillion that I'm keep banging on about.

So in JavaScript, we have a maximum and minimum safe into jail, and that's that nine quadrillion value.

But if we move me on those values, things get a little bit weird.

All right?

We've got a maximum safe into Joe.

We just pay attention to the lost three digits.

Because the rest of it it's just too much.

Um, it ends in 991 All right, let's try to do some maths.

All right?

Working so far.

Um, okay.

Back on track.

Ah, um, I don't know about that.

So the arithmetic just stops adding up at a certain point.

Oh, and so this big number problem is actually what inspired this talk.

Um, and now we're gonna get into beyonc?

Promise Show.

You've all been waiting with bated breath.

Um, so at work.

So for a bit of context at Jack's, tha, um, we're building a massive database of music credits so you can look up your favorite song and see who wrote, Produced, recorded, whatever.

Um, and you can see all the names and click through whatever so work One day I was working on a page.

Let's say I was looking at drunk in love by beyonc?

Which happens to be one of my favorite carrier G songs.

Um, if anyone's interested later, maybe we could make it happen.

Um, also in case you didn't understand the reference of my ship because he weren't familiar with Beyonce's discography.

This is the reference, Um, yeah, beyonc, SS.

It's cool.

Okay, so this is the page for drunk in Love by beyonc?

On Jackson?

Um, that you might notice something a bit weed in that credits panel on the lift is it?

Fiance is both the featured artist and the main artist, which is not really true, because Jay Z's the featured artist on that song.

Um, I mean, to me, this is a feature more than a bug, but, um double Beyonce a hell?

Yeah.

Cool.

Oh, so I noticed that we had this duplicate daughter rendering on the page.

Um, and Beyonce, I wouldn't like this, right.