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Numeric
10:57Let's explore numbers and some basic math operations
[MUSIC]
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We've seen how Python can work with
different types of information, right?
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Like, for instance, so
far we saw strings, and
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we also saw how we could
work a bit with numbers.
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Now, those are definitely
different types of information.
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The more common way you'll hear
this information referred to,
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is with the term data.
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So, these different types of
data are called data types.
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Earlier, I showed off a little bit
of how to work with numbers, or
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rather, numeric data.
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Let's pop open the Python Shell and
dive a little deeper into our exploration.
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So let's go ahead and open up that REPL,
so we do that by typing python.
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I'm gonna scroll this up so
we get some more space.
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Okay, so
whole numbers like 1 are called integers.
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And they're whole because
they aren't fractional,
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meaning they don't have a decimal point.
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So we can add 1 + 2.
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And integers are also called ints for
short, I-N-T, int.
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And we can subtract using the minus key.
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So you do 3 - 2, and
we'll see that we get 1.
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Now, integers can also be negative.
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So we can say 5 - 7, and
that will give us a -2.
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And we can multiply by using the asterisk.
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So 4 * 2 is 8.
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A handy trick that I'd like to show
while we're here is that there's a magic
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variable in the REPL that
always gets set to the result
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of each one of these statements.
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It's stored in the underscore, so, for
instance, this 8 that was just returned,
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it's actually in the variable underscore,
8.
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You'll thank me later when you need that.
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So let's take a look at what happens
when we use a decimal point now.
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So, let's add 4 and we'll do one and
a half, so 1.5.
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Now note, that this returned 5.5.
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This result is not an integer.
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Integers are whole numbers.
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This has a decimal point.
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This is a different data type.
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It's known as a floating-point number,
or float for short.
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Now, we always will get
a float when we do division,
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we'll always be returned to float.
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So watch, this is 16 / 4, and
you'll see that we got 4.0.
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Floats are required when
we need more precision,
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that precision however comes
with a need for some caution.
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As you'll see here, you can do math with
floats just like we were doing with ints.
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So we can say 0.1 + 0.1, and we get 0.2.
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But you need to be careful,
here watch this example.
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So I'll use the history
we'll get back 0.1 + 0.1,
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I'm gonna add one more, so
you can chain values like that.
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You can keep on adding.
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So we get 0.1 + 0.1 + 0.1.
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So that should be 0.3, and
if we subtract 0.3, watch what happens.
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And we get back 5 and some change,
which is weird, right?
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Cuz that should be 0.
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But really, if you look at the end here,
this is exponential, right here.
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This is an exponent of -17,
so this is actually
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5.5 raised to the negative 17th power.
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So, this is really 0 point and
then 17 0s, and then a 5.
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Which is more or less 0 right?
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If you wanna bring a floating point
number back to an integer, you can
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round it to the closest integer using
quite intuitively a function named round.
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So we'll say round,
kind of want to type that.
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I can use the underscore,
so we'll say that, so
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that will be rounding of the 5.55,
blah, blah, blah.
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So here we go, 0, awesome.
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So, I'm gonna do a Ctrl+L here,
that's gonna bring us back up to the top.
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Okay so here we go, so
in case you've forgotten about rounding,
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if the fraction portion is more than half,
it will roll up.
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So we'll say round (4.6), so
that should round to 5, and it does.
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And if its below half, so let's say
4.2 that will round down, awesome.
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Now, these rounding errors have
been a plot point in several movies
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about computer programmers.
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My favorites include Office Space,
where the rounding errors were
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sending fractions of a set to Samir and
Michael Bolton's bank accounts.
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And then the amazing Richard Pryor,
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prior to that pulled a similarly
clever stunt in Superman III.
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Now this points out that floats
in their precisions make them
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not the most ideal type
to deal with currency.
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There are Python data types and various
methods that help to make sure that we
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don't let this movie plot disaster
happen to the software you create.
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There's more in the teacher's notes.
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And you might remember from your math
class, whenever that might have been, but
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there is an order of operations,
and that holds true here too.
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So, we've got this PEMDAS, or
Please Excuse My Dear Aunt Sally,
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that's what my junior high
math teacher used to say.
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So, shout out to Mr. Beetle,
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that one's been stuck in my
head since seventh grade.
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The operations work in that order.
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Now first it's any P which is parenthesis,
then it's E for
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exponents, M for multiplication,
then division, addition, subtraction.
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Now there's more in the teacher's notes
if you feel like you need a refresher.
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Let's just go ahead and
create some random equation.
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Let's do 10 - 3 * 5 + 8.
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So here, using the order of operations,
the multiplication would happen first,
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right?
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So there's no parentheses,
there's no exponents.
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There is an M, so that would happen first.
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And then division, and
then addition, and subtraction.
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So, what we have here is we have 15, and
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we have 10- 15, -5, + 8 is 3.
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Awesome.
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But that's probably not that obvious
if you don't remember the rules.
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So it's best to just be explicit in what
you want and Python lets you do that.
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So, you can just use parenthesis
to drip your ordering.
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Like let's say that we actually
wanted to have 10 - 3 first, so
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I can put that in parens, and
then I wanted to multiply 5 plus 8.
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That way we don't need to,
I think that's more clear, right?
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So we have (10- 3),
we 7 times (5 + 8), is 13.
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I'm gonna go ahead and let that do it,
it should be somewhere around 91.
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There we go, and you can see how
that reads more clear, right?
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Especially the more time that you
spent away not doing math like this.
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Like for instance, over the weekend,
I was talking with my dad's sister and
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she was saying how she forgot
a bunch of this math knowledge.
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So I think that she's a really great
example of how it would help her if you
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were just more explicit with
your mathematical statements.
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I guess what I'm trying to say here
is Please Excuse My Dear Aunt Sally,
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it's been a while for her.
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Bam, math teacher joke, Mr.
Beattle would be so proud.
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Integers and floats working
together is totally convenient
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because the types understand
how to work together.
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But what happens if you try to do
math operations with data types that
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just don't get each other?
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Well, we're here in the REPL,
the place built for exploration.
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So let's just quench our thirst for
knowledge by giving it a try.
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We're not gonna break anything.
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So, let's take the string apple.
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And say "apple, and
I wanna, that's not good.
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We want "apple", and
then I want to add 2 to that.
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So we get a TypeError, and
it must be a string, not an int.
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And that's true,
even if the string looks like a number.
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So if we have "11" + 2.
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That's also a TypeError.
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Now if you remember, our input
function always returns a string.
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I sense that that's gonna be a problem,
because I'm sure eventually we're gonna
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want to prompt a user for a number,
but we're gonna get a string back.
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Gonna CTRL+L to get back up there.
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There is a handy built-in
function that lets you change or
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coerce into a different type.
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So if we want an integer,
we just pass it our string like this.
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So we say int, and we pass in our string.
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So our string 11.
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We'll come back, and
you'll see now it's an int.
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And there's also one for floats.
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So if we could take a float and
we can give it a string of 11,
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and you'll see it comes back with 11.0.
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Awesome, and you can also convert
an existing integer to a float.
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So we'll just give it an 11 there.
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Just straight 11 and a number.
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That's an integer, right?
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And now it becomes 11.0, and,
of course, there's the reverse.
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So if I say int(11.9),
you'll see that we get back 11.
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Now note, this didn't round.
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If it did round, it would be 12 right?
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It would round up.
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What this type of coercion
does is it just forgets
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everything after the decimal point.
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Which might be handy if you only
want to work with integers.
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You can do something similar with
what's known as the division shortcut.
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Remember, division was
a single forward slash.
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So, if we said 23 / 3, and
also we get 7.6 and some change, right?
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That's a float, but
if we use the double forward slashes.
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So, if we say 23 // 3,
we'll get just the integer portion.
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So, we'll get back 7, and if you wanted
to get the remainder in integer form,
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you can do that too using
what is known as the modulus.
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So we'll say 23 % 3.
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So, 3 goes in to 23 7 times,
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and 3 times 7 is 21, right?
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So, 23 minus 21 is our answer too.
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So, that's remainder math.
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More on the teacher's notes.
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That was a lot, right?
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Especially if you're
like my aunt Sally and
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it's been a while since
your last math session.
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Now, don't fear though,
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a common misconception is that there
is a ton of math in all of programming.
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No, don't get me wrong,
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there are defintely heavy calculations
requiring a few business sectors.
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But you'll ramp up to those
calculations as you need them.
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Now if you're working on a shopping cart
application, maybe you'll need some basic
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arithmetic like quantity multiplied
by the price of the product, and
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then calculate tax and
add a shipping charge.
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But those formulas,
they're already established and
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you just need to make the code
run through the proper equations.
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If this all feels overwhelming,
don't worry.
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I'm gonna be walking you through some
practical math examples in this course.
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You got this.
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Why don't we take a well deserved
break and then swing back and
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take a look at our next type, strings.
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