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There are several ways to define a number in JavaScript. In this video we take a look at the syntax for creating several types of numbers in JavaScript.

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[? Music ?] [Treehouse]

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In the last video, we saw some simple ways to define JavaScript

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numbers in our programs.

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Now we'll take a look at a few more advanced techniques

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for creating numbers.

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We've seen how to create numbers using different literals in JavaScript.

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We've created whole numbers, floating point numbers, and negative numbers,

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and we've seen the different rounding errors that can result from

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doing operations on our floating point numbers.

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There are a couple of other ways that we can create numbers

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in our JavaScript files.

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One way we can do this is using a different type of literal

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for our JavaScript numbers, and this one is useful for,

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for instance, very large numbers.

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Say we wanted to represent the number 1 million.

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Well, one way we could do that is by typing in, let's say,

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"g = 1" with 6 zeros after it.

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And if we go into our browser, refresh the page,

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and take a look at our variable g, we'll see that it's 1 million.

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But this isn't a very great way to represent our number.

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There's a lot of zeros next to each other, and we have to really get in there

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and count to figure out what the number is.

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Instead we can use an exponential representation of this number.

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Instead of thinking of it as a 1 with 6 zeros after it,

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we can think of it in scientific notation as 1 times 10 to the sixth power.

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10 to the sixth power is 1 million,

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but that's how we would represent it, so how we can do this

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instead of having our 6 zeros at the end

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is we'll do 1E and then the number 6 for the sixth power.

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And if we go back to our browser and we refresh our page

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and type in the letter "g," we can see the number is also 1 million.

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Now, we don't have to just have the number 1 before our e here.

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We could do 1.23, and that would be 1.23 times 10 to the sixth power,

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so it would be 1,230,000, hopefully.

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If we save it out and refresh, and now if we type "g,"

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we can see we get 123 with 4 zeros after it.

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This allows us to create very large numbers

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without creating very large JavaScript literals in our code,

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so we could extend this out even to the 16th power,

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and if we refresh and take a look at g,

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we can see we have a very large number that we didn't have to manually type out.

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It's both easier to read and less errorprone in our JavaScript code.

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Here's a curious example.

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Let's take the variable h, and I'm going to use the literal 012.

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Now, if you look at this code, you might assume that its value

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is the number 12 or 1 dozen, but if we go back to our code,

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and remember, this is a variable called "h,"

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and we refresh, we see when we type in "h" the number is 10.

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Now, why would this be?

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Well, because our JavaScript literal began with the number 0,

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it actually is being interpreted as an octal number.

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What does this mean?

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Well, normally when we think about numbers, we think about it in the decimal system,

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meaning it's base 10, so we use the digits 0,1,2,3,4,5,6,7,8,9.

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And then when we go above that, we use the next digit to the left,

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put a 1, and start back at 0, so each place in our number

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represents a power of 10.

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However, in octal, each place in our number

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represents a power of 8,

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so instead of using the numbers 0 through 9,

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instead we use the numbers 0 through 7,

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and then when we go to the number above 7,

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instead of representing it with the digit 8,

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we instead move to the left, set its value up 1,

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and then use a 0, so instead of going 6,7,8,

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in octal you would go 6,7,1,0 or 10,

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even though 1,0 would actually be the representation of 8 in octal.

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When we see 012, we're seeing octal,

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and we can calculate its number.

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By seeing the 1 in the second to last place,

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we can see that means 8, and then in the last place we see 2,

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so we can add 8 + 2, and its actual value number is 10.

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Now, using octal numbers isn't something that you would do very often in code.

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However, this mistake can show up in your code and be very, very confusing.

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You'll wonder why you typed in one number and it seems to be representing a different one.

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Well, that's just because the 0 puts it in a different base,

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so the resolution to this issue is to not lead your JavaScript numbers with a 0

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because that has a very specific meaning, which will cause a lot of confusion.

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Here's another issue with octal.

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012 here is being read as an octal number representing the number 10.

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However, if we change the digits from 012 to 019,

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what would happen?

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Well, because we're starting with a 0, we think we're in octal.

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However, because the number 9 is not used in octal notation

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because the highest digit we can use is 7,

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then we would have a problem.

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You would hope that this would have some sort of error,

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but instead, if we go back to our code and check the value of h now,

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it's 19, so again, we see starting with a 0 we think it's octal,

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however, we see an illegal octal character, so JavaScript interprets it

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as a decimal literal 19.

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It's very confusing, so the moral of this is do not lead

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your JavaScript literals with 0 because it will lead to some very confusing results.

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Now, we've seen that JavaScript can handle literals in both decimal

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and octal notation, which we've seen here.

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There's actually one more base that JavaScript can handle number literals for,

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and that's hexadecimal.

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Now, hexadecimal numbers are base 16.

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You may have seen hexadecimal numbers, for instance,

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when working with colors in CSS.

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For instance, when you represent red,

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the number you would use is ff0000.

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This is actually a number, but it's a base 16 number,

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and you can think about the color red split up like this.

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The first 2 digits represent a number that represents the red value.

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The next 2 digits would have been the green value,

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and the next 2 digits would have been the blue value.

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FF actually represents a number, in this case, 255.

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But we can actually represent this in our JavaScript literal.

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The way we do this is we'll create our variable i here,

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and we'll lead it with a 0 but also lead it with a lowercase x,

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and the 0x represents that we're going to have our literal be in hexadecimal notation,

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and this means our characters can be not just 0 through 9

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but also a through f, so if we typed in ff

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and we check the value of i, we see the number is 255.

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By changing these numbers around, we can do f0

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and see that i is 240.

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And if we wanted to just see what the value of f would be,

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we can refresh, check our value of i,

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and see f represents the number 15.

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When you add 1 to that, it would become 16,

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and 16, when represented in hexadecimal, is 10

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because that's the base of hexadecimal.

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If we save this and refresh, 0x10 should represent 16.

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This could be useful. You don't use it very often.

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But sometimes you do want to represent a number in hexadecimal form,

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so if you ever do, this is a way that you can do it.

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Now we've seen all the different ways that we can define numbers in JavaScript.

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Up next, we'll see some of the things that we can do with those numbers.

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