[MUSIC]. 
Well welcome to class today we're 
going to start you on your journey of 
learning how to program the Python. 
Today's lesson is fairly straight 
forward, you've probably seen some of 
this in middle school and high school 
algebra. 
I'm going to tell you how numbers are 
represented in Python and we will discuss 
how to do arithmetic expressons by 
combining these numbers. 
I don't think its anything that's too 
mysterious here. 
Kind of what you should, what you should 
think about today's lecture is Python is, 
is an over grown calculator. 
We're going to give it some data, in this 
case, numbers and we're going to ask it 
to do some operations. 
And its going to, when its finished, give 
us an answer. 
So that will kind of consume most of 
today's lecture. 
And I'll go on about ways to build 
variables and functions and things like 
that later on. 
Okay let's go to class. 
Before we jump into the details of our 
lecture on Arithmetic Expressions. 
Let me show you about how we're going to 
handle examples that we're going to 
consider during lecture. 
So here I have a code sculptor window 
setting, and it's got the example we're 
going to consider here. 
This is actually a completed example. 
I'm going to walk through it and fill in 
all the Python expressions dynamically so 
you can see how I, how I do it. 
But the critical thing is we're going to 
make that file available to you. 
It's going to, in the break between this 
segment of the video and the next, we're 
going to popup a URL that you can click 
on. 
And it will take you to this file inside 
code sculptor, and you can kind of see up 
here there's actually a naming convention 
we have. 
It's always codesculptor.org. 
We put a hash mark with examples, and 
then afterwards we'll have a lecture 
called .py. 
And you don't have to remember that, the 
link will be here, you can click on it to 
pull it up. 
And you can play around with it either 
during the video or after the video is 
over. 
All right, let's talk about numbers and 
their arithmetic expressions. 
So to begin, let's just dive right in and 
have Python print out some numbers. 
So let's print 3 and -1 and 3.14159 and 
maybe -2.8. 
So if I hit Run here, sure enough out 
come those numbers. 
Now the thing to note is that in Python 
there are actually two types of numbers. 
There's kind of sign whole numbers, 
things like 3 and -1. 
And then there are decimal numbers that 
kind of have fractional parts and always 
have a decimal point. 
And in Python those sign home numbers are 
called ints or integers and kind of the 
decimal numbers are called floats or 
floating point numbers. 
And if you are ever in any doubt about 
kind of what kind of number you are 
working with. 
There is a function in python which can 
actually tell you what type of number you 
are working with is called type. 
So I could say type 3, or maybe type 
3.14159. 
If I run that, well, I'm going to guess 
this is an int and this is a float. 
Let's run it, sure enough, it's an int, 
this is a float. 
Now here's a little trickier test. 
What happens if we ask for the type of 
3.0? 
Now if you look at it, really it's 
kind of it's really a whole number, but 
somehow its kind of got this 0 fractional 
part. 
So in Python this is going to be a float 
in fact the way we are going to be 
working with float is we always have a 
decimal point here, .0. 
Now there's some functions that we can 
use to move back and forth between ints 
and floats and they're not too 
complicated. 
in fact, they're just a function int and 
float. 
So, I could convert something that is a 
floating point number into an integer in 
the following manner. 
[SOUND]. 
And so, these are going to return back 
some integers, and kind of what integer 
are we always going to get? 
Well, the rule is we're going to get a, 
the whole part of this decimal number, 
here. 
So, we're just going to throw away the 
part to the right of the decimal point. 
we can also go through and convert, an 
integer into a float. 
And that again seems kind of crazy, 
because, well, an integer kind of is a 
decimal number but what you're going to 
see is the way Python represents this is. 
We're always going to put .0 here. 
Okay, so when you see 3.0, that's really 
telling you this is a float, -1.0, that's 
a float. 
Now before we move on to talk about 
arithmetic operations, let me give you a 
few words of wisdom about dealing with 
floating point numnbers. 
floating point numbers are only an 
approximation to a decimal number. 
For example, when you do 1 divided by 3, 
you expect the decimal representation of 
something like 0.33333333 with 3 peats 
forever. 
Computers are not really graded 
representing that kind of information. 
In fact a number like pi doesn't even 
have kind of,1 even a nice repeating 
representation. 
There's a famous episode of Star Trek 
where Mister Spock calms rebellious 
computer. 
By asking the computer to compute the 
value of pi to the last decimal digit. 
And the computer whirs off and goes into 
an involute, desperately trying to 
compute the last digit of pi. 
Now, if you'd, the computer people who 
have built the computer have taken this 
class. 
They've no just have a time-out here or 
there. 
But the critical question is kind of what 
goes on inside Python whenever you give 
it a number that has lots of digits. 
What does Python do? 
So let my show you, I had two examples 
real quick here to help you understand. 
So what I've gone out to done is I've 
actually grabbed two really good 
approximations for pi and the square root 
of 2. 
So here I have, this is kind of a 50 
digit approximation of pi, and then I've 
also gone and grabbed a 50 digit 
approximation to the square root of 2. 
So I'm going to actually ask Python now 
to print these out. 
And when you do that, notice that I lost 
a lot of digits here. 
All these digits here kind of got trimmed 
down. 
All these digits here got trimmed down. 
So what happens inside Python is they, 
they represent floating point numbers 
with about 15 decimal digits of accuracy. 
So anything beyond that gets thrown away. 
So, in particular, occasionally when 
you're doing arithmetic operations using 
floating-point numbers. 
You're going to get answers of the form 
four point and a bunch of zeroes and then 
maybe a three at the end. 
What you're seeing here is called, 
something called floating point error. 
Whereas Python is doing the computation. 
It can't do the exact, precise operation 
which you're specifying. 
It can't compute pi to the last decimal 
point, or one-third to the last decimal 
point. 
So, it has to do some approximation. 
So, you're seeing that approximation 
error inside that computation. 
Alright, we've talked about numbers in 
Python lets take about the arithmatic 
operators you have available to do 
computations in Python. 
here's a list of, kind of, basic 
arithmetic operators, we have plus, 
minus, times, division, power, it's 
fairly straight forward. 
You just take two numbers and apply the 
operator to them, so we could say 
something like, 1 plus 2, or 3 minus 4 
are 5 times 6 are 2 to the 5th power. 
And if we run that, out comes 3 minus 1, 
30 and to the 5th is 32. 
one operator that you should pay 
attention to in Python is division. 
So, the, the way the division operator 
works in Python 2 is different in the way 
it works in Python 3. 
In Python 2, if one of the operators is a 
floating point number, then the result of 
division is also a floating point number. 
And it approximates the actual division. 
So, for example, I could say print 1.0 
divided by 3 or 5.0 divided by 2.0 or 
minus 7 divided by 3.0. 
And what would come out when I run that 
is what I'd expect kind of a decimal 
approximation of 1 3rd, 5 halves and kind 
of minus 7 thirds. 
notice at 5, both the operators are 
actually integers. 
Well, Python returns kind of the integer 
version of the answer. 
That particular case is the kind of the 
next lowest integer after you do the 
exact division. 
So for example if I say print 1 divided 
by 3 or 5 divided by 2 or -7 divided by 
3. 
That, the answer comes out to be, well, 1 
integer divided by 3 is 0, we kind of 
round it down, 2.5, then let's see, 5 
divided by 2. 
Integer answer would be 2 here, we kind 
of rounded 2.5 down. 
We do -7 divided 3, well, integer 
division is actually minus 1 3rd. 
And we'll actually talk about division 
more later on, when we talk about 
remainders. 
And we'll have the second operator 
called, slash, slash is explicitly 
integer division. 
All right, we know about numbers, we know 
about arithmetic operators. 
Now, we're ready to build arithmetic 
expressions. 
So, the idea is fairly simple. 
An arithmetic expression is either a 
number or it's an arithmetic operator 
applied to two arithmetic expressions. 
This is kind of our first example of kind 
of recursive definition. 
So for example, 2 it's an arithmetic 
expression, 2 plus 3, it's an arithmetic 
expression. 
Because we've applied the plus operator 
to two arithmetic expressions, 2 and 3. 
Now in practice, you don't really need to 
understand that definition. 
You can just simply go through and type 
in expressions that you're used to using 
from say, middle school algebra. 
So, I could say 1 plus 2 times 3 or 4.0 
minus 5.0, divided by 6.0, or 7 times 8 
plus 9 times 10. 
And if I hit Run, what comes out is 
exactly what I'd expect. 
now, you might kind of say well how did I 
go from this definition kind of involving 
an arithmetic expression. 
Is an arithmetic expression combined with 
operators to this thing that I just typed 
in that's just kind of this flat 
expression. 
I typed in 1 plus 2 times 3. 
So somehow Python knew that this is 
really 1 plus, then 2 times 3. 
Turns out there's this notion of 
precedence. 
You probably studied this in middle 
school algebra, and in fact, you probably 
have a mnemonic you learned at one point, 
maybe remember, which was. 
Please excuse my dear aunt sallie. 
So the first letter of that phrase, of 
each word of that phrase gives us the 
order. 
In which we should do operations when we 
are taking kind this linear version of an 
expression trying to think about in terms 
this kind of recursive definition. 
So it says that we are value an 
expression, we should always do 
parenthesis first and then after that we 
should always do exponentiation next. 
Then we should go through and do 
multiplication and division, M and D. 
And in fact, those have equal precedence. 
So if we have a sequence of those, we 
just do em from left to right. 
And then finally we do addition and 
subtraction last. 
So, for example, let's type in a 
expression here say print, 1 times 2, 1 
times 2 plus 3 times 4. 
And if you look at that, the rules of 
Preston say we should do multiplication 
before addition, so this is really the 
same thing as 2 plus 12. 
So if I run that, sure enough I get 14 
back for both of them. 
And notice here's kind of the real rule, 
which is if you're in doubt about the 
order in which operations take place. 
You can always just go through and use 
parenthesis. 
For example, if I wanted to do that 2 
plus 3 first, I can say 1 plus 1 times, 2 
plus 3 times 4, that should be the same 
thing as 1 times 5, times 4. 
And sure enough these both evaluate to 
20. 
So in practice working with arithmetic in 
expressions inside Python is very 
intuitive. 
It's really what you, what you learn in 
middle school Algebra. 
So I don't think you'll find anything 
real too tricky here. 
So, go ahead and take a shot at it.