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Let's explore numbers and some basic math operations
Update
At 3:22 of the video it is stated "5.5 raised to the negative 17th power". That should actually be: "5.5 times 10 raised to the negative 17th power".
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[MUSIC]
0:00
We've seen how Python can work with
different types of information, right?
0:04
Like, for instance, so
far we saw strings, and
0:08
we also saw how we could
work a bit with numbers.
0:10
Now, those are definitely
different types of information.
0:12
The more common way you'll hear
this information referred to,
0:15
is with the term data.
0:19
So, these different types of
data are called data types.
0:20
Earlier, I showed off a little bit
of how to work with numbers, or
0:25
rather, numeric data.
0:28
Let's pop open the Python Shell and
dive a little deeper into our exploration.
0:30
So let's go ahead and open up that REPL,
so we do that by typing python.
0:35
I'm gonna scroll this up so
we get some more space.
0:40
Okay, so
whole numbers like 1 are called integers.
0:43
And they're whole because
they aren't fractional,
0:50
meaning they don't have a decimal point.
0:52
So we can add 1 + 2.
0:54
And integers are also called ints for
short, I-N-T, int.
0:57
And we can subtract using the minus key.
1:03
So you do 3 - 2, and
we'll see that we get 1.
1:07
Now, integers can also be negative.
1:11
So we can say 5 - 7, and
that will give us a -2.
1:13
And we can multiply by using the asterisk.
1:17
So 4 * 2 is 8.
1:20
A handy trick that I'd like to show
while we're here is that there's a magic
1:23
variable in the REPL that
always gets set to the result
1:26
of each one of these statements.
1:31
It's stored in the underscore, so, for
instance, this 8 that was just returned,
1:33
it's actually in the variable underscore,
8.
1:37
You'll thank me later when you need that.
1:41
So let's take a look at what happens
when we use a decimal point now.
1:43
So, let's add 4 and we'll do one and
a half, so 1.5.
1:48
Now note, that this returned 5.5.
1:55
This result is not an integer.
2:00
Integers are whole numbers.
2:03
This has a decimal point.
2:05
This is a different data type.
2:07
It's known as a floating-point number,
or float for short.
2:08
Now, we always will get
a float when we do division,
2:13
we'll always be returned to float.
2:16
So watch, this is 16 / 4, and
you'll see that we got 4.0.
2:18
Floats are required when
we need more precision,
2:25
that precision however comes
with a need for some caution.
2:28
As you'll see here, you can do math with
floats just like we were doing with ints.
2:32
So we can say 0.1 + 0.1, and we get 0.2.
2:37
But you need to be careful,
here watch this example.
2:42
So I'll use the history
we'll get back 0.1 + 0.1,
2:46
I'm gonna add one more, so
you can chain values like that.
2:49
You can keep on adding.
2:53
So we get 0.1 + 0.1 + 0.1.
2:54
So that should be 0.3, and
if we subtract 0.3, watch what happens.
2:57
And we get back 5 and some change,
which is weird, right?
3:04
Cuz that should be 0.
3:09
But really, if you look at the end here,
this is exponential, right here.
3:10
This is an exponent of -17,
so this is actually
3:16
5.5 raised to the negative 17th power.
3:21
So, this is really 0 point and
then 17 0s, and then a 5.
3:25
Which is more or less 0 right?
3:31
If you wanna bring a floating point
number back to an integer, you can
3:33
round it to the closest integer using
quite intuitively a function named round.
3:36
So we'll say round,
kind of want to type that.
3:42
I can use the underscore,
so we'll say that, so
3:45
that will be rounding of the 5.55,
blah, blah, blah.
3:48
So here we go, 0, awesome.
3:51
So, I'm gonna do a Ctrl+L here,
that's gonna bring us back up to the top.
3:55
Okay so here we go, so
in case you've forgotten about rounding,
4:00
if the fraction portion is more than half,
it will roll up.
4:03
So we'll say round (4.6), so
that should round to 5, and it does.
4:07
And if its below half, so let's say
4.2 that will round down, awesome.
4:12
Now, these rounding errors have
been a plot point in several movies
4:19
about computer programmers.
4:23
My favorites include Office Space,
where the rounding errors were
4:24
sending fractions of a set to Samir and
Michael Bolton's bank accounts.
4:27
And then the amazing Richard Pryor,
4:31
prior to that pulled a similarly
clever stunt in Superman III.
4:33
Now this points out that floats
in their precisions make them
4:37
not the most ideal type
to deal with currency.
4:40
There are Python data types and various
methods that help to make sure that we
4:43
don't let this movie plot disaster
happen to the software you create.
4:46
There's more in the teacher's notes.
4:50
And you might remember from your math
class, whenever that might have been, but
4:52
there is an order of operations,
and that holds true here too.
4:57
So, we've got this PEMDAS, or
Please Excuse My Dear Aunt Sally,
5:00
that's what my junior high
math teacher used to say.
5:13
So, shout out to Mr. Beetle,
5:18
that one's been stuck in my
head since seventh grade.
5:19
The operations work in that order.
5:22
Now first it's any P which is parenthesis,
then it's E for
5:23
exponents, M for multiplication,
then division, addition, subtraction.
5:28
Now there's more in the teacher's notes
if you feel like you need a refresher.
5:33
Let's just go ahead and
create some random equation.
5:36
Let's do 10 - 3 * 5 + 8.
5:39
So here, using the order of operations,
the multiplication would happen first,
5:46
right?
5:51
So there's no parentheses,
there's no exponents.
5:51
There is an M, so that would happen first.
5:54
And then division, and
then addition, and subtraction.
5:56
So, what we have here is we have 15, and
5:59
we have 10- 15, -5, + 8 is 3.
6:03
Awesome.
6:07
But that's probably not that obvious
if you don't remember the rules.
6:08
So it's best to just be explicit in what
you want and Python lets you do that.
6:13
So, you can just use parenthesis
to drip your ordering.
6:17
Like let's say that we actually
wanted to have 10 - 3 first, so
6:21
I can put that in parens, and
then I wanted to multiply 5 plus 8.
6:25
That way we don't need to,
I think that's more clear, right?
6:30
So we have (10- 3),
we 7 times (5 + 8), is 13.
6:33
I'm gonna go ahead and let that do it,
it should be somewhere around 91.
6:39
There we go, and you can see how
that reads more clear, right?
6:43
Especially the more time that you
spent away not doing math like this.
6:46
Like for instance, over the weekend,
I was talking with my dad's sister and
6:50
she was saying how she forgot
a bunch of this math knowledge.
6:55
So I think that she's a really great
example of how it would help her if you
6:58
were just more explicit with
your mathematical statements.
7:01
I guess what I'm trying to say here
is Please Excuse My Dear Aunt Sally,
7:04
it's been a while for her.
7:08
Bam, math teacher joke, Mr.
Beattle would be so proud.
7:10
Integers and floats working
together is totally convenient
7:13
because the types understand
how to work together.
7:17
But what happens if you try to do
math operations with data types that
7:20
just don't get each other?
7:23
Well, we're here in the REPL,
the place built for exploration.
7:25
So let's just quench our thirst for
knowledge by giving it a try.
7:28
We're not gonna break anything.
7:32
So, let's take the string apple.
7:33
And say "apple, and
I wanna, that's not good.
7:37
We want "apple", and
then I want to add 2 to that.
7:43
So we get a TypeError, and
it must be a string, not an int.
7:48
And that's true,
even if the string looks like a number.
7:53
So if we have "11" + 2.
7:56
That's also a TypeError.
8:00
Now if you remember, our input
function always returns a string.
8:02
I sense that that's gonna be a problem,
because I'm sure eventually we're gonna
8:07
want to prompt a user for a number,
but we're gonna get a string back.
8:10
Gonna CTRL+L to get back up there.
8:15
There is a handy built-in
function that lets you change or
8:17
coerce into a different type.
8:21
So if we want an integer,
we just pass it our string like this.
8:23
So we say int, and we pass in our string.
8:27
So our string 11.
8:30
We'll come back, and
you'll see now it's an int.
8:31
And there's also one for floats.
8:35
So if we could take a float and
we can give it a string of 11,
8:36
and you'll see it comes back with 11.0.
8:39
Awesome, and you can also convert
an existing integer to a float.
8:42
So we'll just give it an 11 there.
8:46
Just straight 11 and a number.
8:48
That's an integer, right?
8:49
And now it becomes 11.0, and,
of course, there's the reverse.
8:51
So if I say int(11.9),
you'll see that we get back 11.
8:54
Now note, this didn't round.
9:01
If it did round, it would be 12 right?
9:03
It would round up.
9:05
What this type of coercion
does is it just forgets
9:06
everything after the decimal point.
9:09
Which might be handy if you only
want to work with integers.
9:11
You can do something similar with
what's known as the division shortcut.
9:15
Remember, division was
a single forward slash.
9:19
So, if we said 23 / 3, and
also we get 7.6 and some change, right?
9:22
That's a float, but
if we use the double forward slashes.
9:28
So, if we say 23 // 3,
we'll get just the integer portion.
9:31
So, we'll get back 7, and if you wanted
to get the remainder in integer form,
9:37
you can do that too using
what is known as the modulus.
9:42
So we'll say 23 % 3.
9:46
So, 3 goes in to 23 7 times,
9:51
and 3 times 7 is 21, right?
9:56
So, 23 minus 21 is our answer too.
10:00
So, that's remainder math.
10:02
More on the teacher's notes.
10:04
That was a lot, right?
10:09
Especially if you're
like my aunt Sally and
10:10
it's been a while since
your last math session.
10:12
Now, don't fear though,
10:14
a common misconception is that there
is a ton of math in all of programming.
10:15
No, don't get me wrong,
10:19
there are defintely heavy calculations
requiring a few business sectors.
10:20
But you'll ramp up to those
calculations as you need them.
10:24
Now if you're working on a shopping cart
application, maybe you'll need some basic
10:28
arithmetic like quantity multiplied
by the price of the product, and
10:32
then calculate tax and
add a shipping charge.
10:35
But those formulas,
they're already established and
10:38
you just need to make the code
run through the proper equations.
10:40
If this all feels overwhelming,
don't worry.
10:44
I'm gonna be walking you through some
practical math examples in this course.
10:47
You got this.
10:50
Why don't we take a well deserved
break and then swing back and
10:52
take a look at our next type, strings.
10:55
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