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This site is a preview of the curriculum for our Summer 2018 bootcamp in Burlington, Vermont. As we continue our preparation, courses and lessons will appear and disappear; we will rename, rearrange, clarify, and obfuscate as needed... Please consider this a work in progress and keep checking in.
Learn to Code with JavaScript:
Numbers
Slides
Number
- JavaScript has a built-in type called
Number
. - It represents decimal numbers, aka floating-point decimals.
- JavaScript does not have a special type for integers, unlike most other languages.
Numbers
The following operations work on numbers:
operand | name | example | = |
---|---|---|---|
+ | addition | 3 + 2 | 5 |
- | subtraction | 3 - 2 | 1 |
* | multiplication | 3 * 2 | 6 |
/ | division | 3 / 2 | 1.5 |
% | modulus ("remainder") | 3 % 2 | 1 |
** | exponentiation ("power of") | 3 ** 2 | 9 |
LAB: Playing With Numbers
Answer the following questions using node
:
- How many seconds are in an hour?
- How many minutes are in a week?
- How many seconds old are you?
- How many years old is someone who is 1 billion seconds old?
Order of operations
Q: What is 1 plus 2 times 3?
Order of operations
Q: What is 1 plus 2 times 3?
A: It depends!
(1 + 2) * 3 == 9 1 + (2 * 3) == 7
Parentheses Are Free
When in doubt, use parentheses!
(or, when there's any doubt, make your assumptions explicit)
LAB: one nation, divisible
One number is divisible by another if you divide them and the remainder is 0.
Write code in node
to figure out if...
- 100 is divisible by 5
- 100 is divisible by 8
- 330 is divisible by 11
- 337 is divisible by 7
Strings vs. Numbers
Hmmm....
1 + 2 "1" + "2" "1 + 2"
Strings plus Numbers
Hmmm again...
"1" + 2
Even though Strings and Numbers are different TYPES, JavaScript converts one to the other.
But when two types meet, which one wins?
Type Conversion
The clearest answer is that you, the programmer, explicitly declare which type you want to win.
Converting a Number to a String
(12).toString() // "12"
Converting a String to a Number
There are many ways to convert a string to a number in JavaScript.
The easiest and cleanest is unary +
:
expression | value |
---|---|
+"12" | 12 |
+"012" | 12 |
+"0.2" | 0.2 |
+"cheese" | NaN |
+"0" | 0 |
+"" | 0 |
+" " | 0 |
(Other ways can give bizarre results if the string contains letters or begins with a 0.)
Type Coercion
If you don't explicitly do type conversion then JavaScript will "helpfully" convert the types for you.
This is called type coercion and just like with people, coercion is stressful and often backfires.
For instance, if you ask the user their age, and read it from a web form or keyboard input, it will be in a string. If you forget to explicitly convert that to a number before using it in a calculation, the results can be unexpected...
> "30" - 1 // "30" is coerced into a number 29 > "30" + 1 // 1 is coerced into a string '301'
(You Don't Know JS has way more information than you wanted to know on this subject.)
Math is hard
There are many types of numbers!
Each is useful in different situations.
In elementary school, we learned
- natural numbers (aka counting numbers)
- integer numbers (naturals, negatives, and zero)
- rational numbers (aka fractions or ratios)
In high school, we learned irrational, complex, and imaginary numbers.
JavaScript numbers are different from all of those!
Floating-Point Numbers
JavaScript numbers...
- use decimal notation
- are stored in binary
- have a fixed bit-length
Some rational numbers cannot be represented in floating-point, which means that simple arithmetic may give unexpected results.
For instance, you can't go higher than about 9 quadrillion without glitching...
> 2**53 == 2**53+1 true
(This problem is not unique to JavaScript, but the fact that all numbers in JS are floating-point means that beginners can't avoid it.)
see Wikipedia on IEEE 754 double aka Double-precision floating-point format or binary64
Arithmetic
Try this in node:
1 + 2 3 - 4 5 * 6 7 / 8 2 / 3 7 / 9
Wait a second...
> 2/3 0.6666666666666666 > 7/9 0.7777777777777778
Why did it round up the last digit for 7/9
but not for 2/3
?
Floating Point Arithmetic is Bizarre
> 7/9 0.7777777777777778 > 0.5 - 0.4 - 0.1 -2.7755575615628914e-17 > (0.8 - 0.7 - 0.1)/(0.5 - 0.4 - 0.1) -3 > 2**53 == 2**53+1 true > 2**10000 Infinity
Okay, that's enough math for now!
Outline
- Number
- Numbers
- LAB: Playing With Numbers
- Order of operations
- Order of operations
- Parentheses Are Free
- LAB: one nation, divisible
- Strings vs. Numbers
- Strings plus Numbers
- Type Conversion
- Converting a Number to a String
- Converting a String to a Number
- Type Coercion
- Math is hard
- Floating-Point Numbers
- Arithmetic
- Floating Point Arithmetic is Bizarre
- Okay, that's enough math for now!
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