02_numbers.md

Numbers in Python

Knowing how to use a programming language like an elaborate calculator is one of the most fundamental skills of programming.

Python has plenty of built-in mathematical functions, as well as some powerful libraries for higher-level math, statistics, etc. that we won't go over today, but might prove useful in the future (e.g., scipy, pandas, matplotlib).

Variables

Before we get into actual math, you'll need to understand variables. Technically, you can do basic math without them, but variables will make your code way simpler and easy to use.

A variable is a name that refers to some value. You can define a variable using an equals sign (=, also known as an assignment operator), and then use it or manipulate it later on in your code.

Variable names can contain letters, numbers, and some special characters (- and _), and must start with a lowercase letter.

In the following example:

x = 5
print(x)

The interpreter would print 5.

Variables in Python are dynamically typed. That means that you can assign an integer value to a variable, and then later on make it a string without encountering an error. (Many other languages are statically typed, meaning that you declare the data type with the variable, and cannot change it later.) So:

x = 5
x = "Hello"
print(x)

The interpreter would print Hello.

Try it yourself: Define some variables

Make a new file called numbers.py

Define a variable a and set it equal to 2. Define another variable b and set it equal to 5.

Save the file. We will use these variables in later steps.

Operations

Python has several basic mathematical operators: +, -, *, /, **, and %.

You can probably guess that + and - are addition and subtraction, respectively.

* is for multiplication, and / is for division—but division has some interesting and useful quirks that we will get to in the next step.

** is for exponentiation; that is, 3**2 is the same as "3 squared."

% is called a modulus (or mod). It is related to division's quirks, so we'll cover it shortly.

Math is generally carried out how you'd expect, in that 2+2 is a valid Python statement.

Try it yourself: Basic operations

Go over to your IPython terminal (if IPython is not running, start it up again) and %run numbers.py.

You won't see any output—that's okay, we didn't include any print statements! Instead, the variables you defined in numbers.py are now in IPython's memory, ready for you to use them. Make sure everything is set by entering a into the prompt. It should return 2.

Now, let's do some math. Enter the following lines into IPython one-by-one, but before you enter each one, try to guess what it'll do.

a+b
a-b
a*b
a**b

Simple enough. Now to mix it up a little:

2*a
42**b
b + 3 * a
a * (a + b) - b**b
10(b)

Sorry, that last one was a trick. You might be used to using parentheses to represent multiplication, but that doesn't work in Python. You still need the *. You can, however, use parentheses for association (like in a * (a + b) - b**b).

Integers, floats, and division

As we currently have them defined, a and b are both integers, meaning that they are numbers that do not contain decimals.

Numbers that do contain decimals (even if the decimal place is ".0") are called floats. This distinction often does not matter, because 5 + 5 and 5.0 + 5.0 are numerically equivalent. But it does matter when considering division, which often has a remainder.

When you divide two floats (or even an integer and a float), everything goes as you would expect, and it returns a float:

1.2 / 2.4

returns 0.5.

But, when you divide two integers, you get an integer. The remainder is discarded.

5 / 2

returns 2.

On the other hand, we have the modulus function (%). This returns only the remainder.

5 % 2

returns 1.

Try it yourself: division

First, go back to numbers.py and define a variable c whose value is 1.5. Then define one more variable, d, and give it a value of 3, but make it a float.

Go back to IPython and %run numbers.py to bring your new variables into memory.

Try these lines, guessing in advance what they will do:

a / b
b / a
a * c
b / c
d / c
b % a
c % a  
a % c

Now, define a variable e (in IPython) whose value is the sum of a and b, divided by the product of c and d. What will the value of e be? What type (integer or float) will e be?

Call type(e) to see if you're right.

That's all for this section!

Next up is 03_boolean-operators.md