Name: Double the Beyoncé: Navigating Numbers in JavaScript by Meggan Turner | JSConf.Asia 2019
Uploaded: 2020-03-28T16:43:53.000Z
Duration: 25 min 38 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

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.

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

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.

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.

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.

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.

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.

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.

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, 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.

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

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.

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

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.

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.

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

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

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%.

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.

Subtitles ListPlay Video

Double the Beyoncé: Navigating Numbers in JavaScript by Meggan Turner | JSConf.Asia 2019

massive

concept

positive

negative