1
00:00:00,154 --> 00:00:07,539
[MUSIC]. 

2
00:00:07,539 --> 00:00:10,548
Well welcome to class today we're 
going to start you on your journey of 

3
00:00:10,548 --> 00:00:15,767
learning how to program the Python. 
Today's lesson is fairly straight 

4
00:00:15,767 --> 00:00:19,925
forward, you've probably seen some of 
this in middle school and high school 

5
00:00:19,925 --> 00:00:23,376
algebra. 
I'm going to tell you how numbers are 

6
00:00:23,376 --> 00:00:26,960
represented in Python and we will discuss 
how to do arithmetic expressons by 

7
00:00:26,960 --> 00:00:31,855
combining these numbers. 
I don't think its anything that's too 

8
00:00:31,855 --> 00:00:35,149
mysterious here. 
Kind of what you should, what you should 

9
00:00:35,149 --> 00:00:39,310
think about today's lecture is Python is, 
is an over grown calculator. 

10
00:00:39,310 --> 00:00:41,933
We're going to give it some data, in this 
case, numbers and we're going to ask it 

11
00:00:41,933 --> 00:00:45,158
to do some operations. 
And its going to, when its finished, give 

12
00:00:45,158 --> 00:00:47,542
us an answer. 
So that will kind of consume most of 

13
00:00:47,542 --> 00:00:50,053
today's lecture. 
And I'll go on about ways to build 

14
00:00:50,053 --> 00:00:53,144
variables and functions and things like 
that later on. 

15
00:00:53,144 --> 00:00:59,429
Okay let's go to class. 
Before we jump into the details of our 

16
00:00:59,429 --> 00:01:03,659
lecture on Arithmetic Expressions. 
Let me show you about how we're going to 

17
00:01:03,659 --> 00:01:07,580
handle examples that we're going to 
consider during lecture. 

18
00:01:09,150 --> 00:01:12,363
So here I have a code sculptor window 
setting, and it's got the example we're 

19
00:01:12,363 --> 00:01:15,570
going to consider here. 
This is actually a completed example. 

20
00:01:15,570 --> 00:01:18,738
I'm going to walk through it and fill in 
all the Python expressions dynamically so 

21
00:01:18,738 --> 00:01:22,866
you can see how I, how I do it. 
But the critical thing is we're going to 

22
00:01:22,866 --> 00:01:25,746
make that file available to you. 
It's going to, in the break between this 

23
00:01:25,746 --> 00:01:28,598
segment of the video and the next, we're 
going to popup a URL that you can click 

24
00:01:28,598 --> 00:01:32,112
on. 
And it will take you to this file inside 

25
00:01:32,112 --> 00:01:36,504
code sculptor, and you can kind of see up 
here there's actually a naming convention 

26
00:01:36,504 --> 00:01:40,940
we have. 
It's always codesculptor.org. 

27
00:01:40,940 --> 00:01:44,234
We put a hash mark with examples, and 
then afterwards we'll have a lecture 

28
00:01:44,234 --> 00:01:47,048
called .py. 
And you don't have to remember that, the 

29
00:01:47,048 --> 00:01:49,697
link will be here, you can click on it to 
pull it up. 

30
00:01:49,697 --> 00:01:52,301
And you can play around with it either 
during the video or after the video is 

31
00:01:52,301 --> 00:01:55,405
over. 
All right, let's talk about numbers and 

32
00:01:55,405 --> 00:01:59,697
their arithmetic expressions. 
So to begin, let's just dive right in and 

33
00:01:59,697 --> 00:02:05,968
have Python print out some numbers. 
So let's print 3 and -1 and 3.14159 and 

34
00:02:05,968 --> 00:02:11,760
maybe -2.8. 
So if I hit Run here, sure enough out 

35
00:02:11,760 --> 00:02:16,464
come those numbers. 
Now the thing to note is that in Python 

36
00:02:16,464 --> 00:02:21,500
there are actually two types of numbers. 
There's kind of sign whole numbers, 

37
00:02:21,500 --> 00:02:25,354
things like 3 and -1. 
And then there are decimal numbers that 

38
00:02:25,354 --> 00:02:29,500
kind of have fractional parts and always 
have a decimal point. 

39
00:02:29,500 --> 00:02:33,064
And in Python those sign home numbers are 
called ints or integers and kind of the 

40
00:02:33,064 --> 00:02:37,326
decimal numbers are called floats or 
floating point numbers. 

41
00:02:37,326 --> 00:02:40,400
And if you are ever in any doubt about 
kind of what kind of number you are 

42
00:02:40,400 --> 00:02:43,607
working with. 
There is a function in python which can 

43
00:02:43,607 --> 00:02:47,648
actually tell you what type of number you 
are working with is called type. 

44
00:02:47,648 --> 00:02:59,018
So I could say type 3, or maybe type 
3.14159. 

45
00:02:59,018 --> 00:03:03,162
If I run that, well, I'm going to guess 
this is an int and this is a float. 

46
00:03:03,162 --> 00:03:06,830
Let's run it, sure enough, it's an int, 
this is a float. 

47
00:03:06,830 --> 00:03:13,010
Now here's a little trickier test. 
What happens if we ask for the type of 

48
00:03:13,010 --> 00:03:16,235
3.0? 
Now if you look at it, really it's 

49
00:03:16,235 --> 00:03:19,755
kind of it's really a whole number, but 
somehow its kind of got this 0 fractional 

50
00:03:19,755 --> 00:03:22,924
part. 
So in Python this is going to be a float 

51
00:03:22,924 --> 00:03:26,002
in fact the way we are going to be 
working with float is we always have a 

52
00:03:26,002 --> 00:03:31,450
decimal point here, .0. 
Now there's some functions that we can 

53
00:03:31,450 --> 00:03:34,585
use to move back and forth between ints 
and floats and they're not too 

54
00:03:34,585 --> 00:03:37,746
complicated. 
in fact, they're just a function int and 

55
00:03:37,746 --> 00:03:41,392
float. 
So, I could convert something that is a 

56
00:03:41,392 --> 00:03:48,204
floating point number into an integer in 
the following manner. 

57
00:03:48,204 --> 00:03:50,838
[SOUND]. 
And so, these are going to return back 

58
00:03:50,838 --> 00:03:55,820
some integers, and kind of what integer 
are we always going to get? 

59
00:03:55,820 --> 00:03:58,687
Well, the rule is we're going to get a, 
the whole part of this decimal number, 

60
00:03:58,687 --> 00:04:00,946
here. 
So, we're just going to throw away the 

61
00:04:00,946 --> 00:04:06,506
part to the right of the decimal point. 
we can also go through and convert, an 

62
00:04:06,506 --> 00:04:13,620
integer into a float. 
And that again seems kind of crazy, 

63
00:04:13,620 --> 00:04:17,280
because, well, an integer kind of is a 
decimal number but what you're going to 

64
00:04:17,280 --> 00:04:24,070
see is the way Python represents this is. 
We're always going to put .0 here. 

65
00:04:24,070 --> 00:04:29,631
Okay, so when you see 3.0, that's really 
telling you this is a float, -1.0, that's 

66
00:04:29,631 --> 00:04:34,238
a float. 
Now before we move on to talk about 

67
00:04:34,238 --> 00:04:38,264
arithmetic operations, let me give you a 
few words of wisdom about dealing with 

68
00:04:38,264 --> 00:04:43,844
floating point numnbers. 
floating point numbers are only an 

69
00:04:43,844 --> 00:04:50,160
approximation to a decimal number. 
For example, when you do 1 divided by 3, 

70
00:04:50,160 --> 00:04:54,580
you expect the decimal representation of 
something like 0.33333333 with 3 peats 

71
00:04:54,580 --> 00:04:58,821
forever. 
Computers are not really graded 

72
00:04:58,821 --> 00:05:05,009
representing that kind of information. 
In fact a number like pi doesn't even 

73
00:05:05,009 --> 00:05:09,780
have kind of,1 even a nice repeating 
representation. 

74
00:05:09,780 --> 00:05:14,395
There's a famous episode of Star Trek 
where Mister Spock calms rebellious 

75
00:05:14,395 --> 00:05:18,188
computer. 
By asking the computer to compute the 

76
00:05:18,188 --> 00:05:22,961
value of pi to the last decimal digit. 
And the computer whirs off and goes into 

77
00:05:22,961 --> 00:05:26,830
an involute, desperately trying to 
compute the last digit of pi. 

78
00:05:26,830 --> 00:05:29,170
Now, if you'd, the computer people who 
have built the computer have taken this 

79
00:05:29,170 --> 00:05:31,198
class. 
They've no just have a time-out here or 

80
00:05:31,198 --> 00:05:34,087
there. 
But the critical question is kind of what 

81
00:05:34,087 --> 00:05:39,820
goes on inside Python whenever you give 
it a number that has lots of digits. 

82
00:05:39,820 --> 00:05:42,460
What does Python do? 
So let my show you, I had two examples 

83
00:05:42,460 --> 00:05:47,229
real quick here to help you understand. 
So what I've gone out to done is I've 

84
00:05:47,229 --> 00:05:51,072
actually grabbed two really good 
approximations for pi and the square root 

85
00:05:51,072 --> 00:05:55,822
of 2. 
So here I have, this is kind of a 50 

86
00:05:55,822 --> 00:06:02,782
digit approximation of pi, and then I've 
also gone and grabbed a 50 digit 

87
00:06:02,782 --> 00:06:12,056
approximation to the square root of 2. 
So I'm going to actually ask Python now 

88
00:06:12,056 --> 00:06:15,112
to print these out. 
And when you do that, notice that I lost 

89
00:06:15,112 --> 00:06:17,818
a lot of digits here. 
All these digits here kind of got trimmed 

90
00:06:17,818 --> 00:06:21,430
down. 
All these digits here got trimmed down. 

91
00:06:21,430 --> 00:06:25,005
So what happens inside Python is they, 
they represent floating point numbers 

92
00:06:25,005 --> 00:06:31,530
with about 15 decimal digits of accuracy. 
So anything beyond that gets thrown away. 

93
00:06:31,530 --> 00:06:34,726
So, in particular, occasionally when 
you're doing arithmetic operations using 

94
00:06:34,726 --> 00:06:37,959
floating-point numbers. 
You're going to get answers of the form 

95
00:06:37,959 --> 00:06:41,978
four point and a bunch of zeroes and then 
maybe a three at the end. 

96
00:06:41,978 --> 00:06:45,203
What you're seeing here is called, 
something called floating point error. 

97
00:06:45,203 --> 00:06:50,393
Whereas Python is doing the computation. 
It can't do the exact, precise operation 

98
00:06:50,393 --> 00:06:54,406
which you're specifying. 
It can't compute pi to the last decimal 

99
00:06:54,406 --> 00:06:58,190
point, or one-third to the last decimal 
point. 

100
00:06:58,190 --> 00:07:02,438
So, it has to do some approximation. 
So, you're seeing that approximation 

101
00:07:02,438 --> 00:07:11,474
error inside that computation. 
Alright, we've talked about numbers in 

102
00:07:11,474 --> 00:07:15,186
Python lets take about the arithmatic 
operators you have available to do 

103
00:07:15,186 --> 00:07:20,082
computations in Python. 
here's a list of, kind of, basic 

104
00:07:20,082 --> 00:07:25,975
arithmetic operators, we have plus, 
minus, times, division, power, it's 

105
00:07:25,975 --> 00:07:33,016
fairly straight forward. 
You just take two numbers and apply the 

106
00:07:33,016 --> 00:07:38,887
operator to them, so we could say 
something like, 1 plus 2, or 3 minus 4 

107
00:07:38,887 --> 00:07:49,507
are 5 times 6 are 2 to the 5th power. 
And if we run that, out comes 3 minus 1, 

108
00:07:49,507 --> 00:07:56,225
30 and to the 5th is 32. 
one operator that you should pay 

109
00:07:56,225 --> 00:08:01,193
attention to in Python is division. 
So, the, the way the division operator 

110
00:08:01,193 --> 00:08:06,040
works in Python 2 is different in the way 
it works in Python 3. 

111
00:08:06,040 --> 00:08:10,261
In Python 2, if one of the operators is a 
floating point number, then the result of 

112
00:08:10,261 --> 00:08:16,493
division is also a floating point number. 
And it approximates the actual division. 

113
00:08:16,493 --> 00:08:23,333
So, for example, I could say print 1.0 
divided by 3 or 5.0 divided by 2.0 or 

114
00:08:23,333 --> 00:08:32,227
minus 7 divided by 3.0. 
And what would come out when I run that 

115
00:08:32,227 --> 00:08:40,345
is what I'd expect kind of a decimal 
approximation of 1 3rd, 5 halves and kind 

116
00:08:40,345 --> 00:08:47,772
of minus 7 thirds. 
notice at 5, both the operators are 

117
00:08:47,772 --> 00:08:52,577
actually integers. 
Well, Python returns kind of the integer 

118
00:08:52,577 --> 00:08:56,848
version of the answer. 
That particular case is the kind of the 

119
00:08:56,848 --> 00:08:59,860
next lowest integer after you do the 
exact division. 

120
00:08:59,860 --> 00:09:08,980
So for example if I say print 1 divided 
by 3 or 5 divided by 2 or -7 divided by 

121
00:09:08,980 --> 00:09:15,646
3. 
That, the answer comes out to be, well, 1 

122
00:09:15,646 --> 00:09:21,369
integer divided by 3 is 0, we kind of 
round it down, 2.5, then let's see, 5 

123
00:09:21,369 --> 00:09:28,642
divided by 2. 
Integer answer would be 2 here, we kind 

124
00:09:28,642 --> 00:09:33,240
of rounded 2.5 down. 
We do -7 divided 3, well, integer 

125
00:09:33,240 --> 00:09:37,271
division is actually minus 1 3rd. 
And we'll actually talk about division 

126
00:09:37,271 --> 00:09:40,060
more later on, when we talk about 
remainders. 

127
00:09:40,060 --> 00:09:43,128
And we'll have the second operator 
called, slash, slash is explicitly 

128
00:09:43,128 --> 00:09:48,956
integer division. 
All right, we know about numbers, we know 

129
00:09:48,956 --> 00:09:55,001
about arithmetic operators. 
Now, we're ready to build arithmetic 

130
00:09:55,001 --> 00:09:58,810
expressions. 
So, the idea is fairly simple. 

131
00:09:58,810 --> 00:10:03,094
An arithmetic expression is either a 
number or it's an arithmetic operator 

132
00:10:03,094 --> 00:10:08,484
applied to two arithmetic expressions. 
This is kind of our first example of kind 

133
00:10:08,484 --> 00:10:12,680
of recursive definition. 
So for example, 2 it's an arithmetic 

134
00:10:12,680 --> 00:10:17,115
expression, 2 plus 3, it's an arithmetic 
expression. 

135
00:10:17,115 --> 00:10:23,027
Because we've applied the plus operator 
to two arithmetic expressions, 2 and 3. 

136
00:10:23,027 --> 00:10:26,524
Now in practice, you don't really need to 
understand that definition. 

137
00:10:26,524 --> 00:10:29,824
You can just simply go through and type 
in expressions that you're used to using 

138
00:10:29,824 --> 00:10:38,195
from say, middle school algebra. 
So, I could say 1 plus 2 times 3 or 4.0 

139
00:10:38,195 --> 00:10:51,980
minus 5.0, divided by 6.0, or 7 times 8 
plus 9 times 10. 

140
00:10:51,980 --> 00:10:56,908
And if I hit Run, what comes out is 
exactly what I'd expect. 

141
00:10:56,908 --> 00:11:00,289
now, you might kind of say well how did I 
go from this definition kind of involving 

142
00:11:00,289 --> 00:11:04,203
an arithmetic expression. 
Is an arithmetic expression combined with 

143
00:11:04,203 --> 00:11:07,143
operators to this thing that I just typed 
in that's just kind of this flat 

144
00:11:07,143 --> 00:11:12,450
expression. 
I typed in 1 plus 2 times 3. 

145
00:11:12,450 --> 00:11:19,000
So somehow Python knew that this is 
really 1 plus, then 2 times 3. 

146
00:11:19,000 --> 00:11:20,800
Turns out there's this notion of 
precedence. 

147
00:11:20,800 --> 00:11:23,855
You probably studied this in middle 
school algebra, and in fact, you probably 

148
00:11:23,855 --> 00:11:28,020
have a mnemonic you learned at one point, 
maybe remember, which was. 

149
00:11:28,020 --> 00:11:31,839
Please excuse my dear aunt sallie. 
So the first letter of that phrase, of 

150
00:11:31,839 --> 00:11:34,691
each word of that phrase gives us the 
order. 

151
00:11:34,691 --> 00:11:38,309
In which we should do operations when we 
are taking kind this linear version of an 

152
00:11:38,309 --> 00:11:43,910
expression trying to think about in terms 
this kind of recursive definition. 

153
00:11:43,910 --> 00:11:46,562
So it says that we are value an 
expression, we should always do 

154
00:11:46,562 --> 00:11:52,130
parenthesis first and then after that we 
should always do exponentiation next. 

155
00:11:52,130 --> 00:11:54,930
Then we should go through and do 
multiplication and division, M and D. 

156
00:11:54,930 --> 00:11:58,347
And in fact, those have equal precedence. 
So if we have a sequence of those, we 

157
00:11:58,347 --> 00:12:01,917
just do em from left to right. 
And then finally we do addition and 

158
00:12:01,917 --> 00:12:08,238
subtraction last. 
So, for example, let's type in a 

159
00:12:08,238 --> 00:12:18,610
expression here say print, 1 times 2, 1 
times 2 plus 3 times 4. 

160
00:12:18,610 --> 00:12:23,398
And if you look at that, the rules of 
Preston say we should do multiplication 

161
00:12:23,398 --> 00:12:29,370
before addition, so this is really the 
same thing as 2 plus 12. 

162
00:12:29,370 --> 00:12:33,397
So if I run that, sure enough I get 14 
back for both of them. 

163
00:12:33,397 --> 00:12:36,799
And notice here's kind of the real rule, 
which is if you're in doubt about the 

164
00:12:36,799 --> 00:12:41,447
order in which operations take place. 
You can always just go through and use 

165
00:12:41,447 --> 00:12:46,955
parenthesis. 
For example, if I wanted to do that 2 

166
00:12:46,955 --> 00:12:56,317
plus 3 first, I can say 1 plus 1 times, 2 
plus 3 times 4, that should be the same 

167
00:12:56,317 --> 00:13:07,646
thing as 1 times 5, times 4. 
And sure enough these both evaluate to 

168
00:13:07,646 --> 00:13:10,832
20. 
So in practice working with arithmetic in 

169
00:13:10,832 --> 00:13:14,220
expressions inside Python is very 
intuitive. 

170
00:13:14,220 --> 00:13:17,020
It's really what you, what you learn in 
middle school Algebra. 

171
00:13:17,020 --> 00:13:20,000
So I don't think you'll find anything 
real too tricky here. 

172
00:13:20,000 --> 00:13:24,013
So, go ahead and take a shot at it.