Lesson 2
Integer and float numbers

1. Integer arithmetics

We already know the following operators which may be applied to numbers: +, -, * and **. The division operator / for integers gives a floating-point real number (an object of type float). The exponentiation ** also returns a float when the power is negative:

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print(17 / 3)  # gives 5.66666666667
print(2 ** 4)  # gives 16
print(2 ** -2) # gives 0.25

There's a special operation for integer division where the remainder is discarded: //. The operation that yields a remainder of such a division looks like %. Both operation always yield an object of type int.

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print(17 / 3)   # gives 5.66666666667
print(17 // 3)  # gives 5
print(17 % 3)   # gives 2

2. Floating-point numbers

When we read an integer value, we read a line with input() and then cast a string to integer using int(). When we read a floating-point number, we need to cast the string to float using float():

1.492

x = float(input())
print(x)

Floats with very big or very small absolute value can be written using a scientific notation. Eg., the distance from the Earth to the Sun is 1.496·10¹¹, or 1.496e11 in Python. The mass of one molecule of the water is 2.99·10^-23, or 2.99e-23 in Python.

One can cast float objects to int objects by discarding the fraction part using the int() function. This function demonstrates so called rounding towards zero behavior:

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print(int(1.3))   # gives 1
print(int(1.7))   # gives 1
print(int(-1.3))  # gives -1
print(int(-1.7))  # gives -1

There's also a function round() that performs the usual rounding:

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print(round(1.3))   # gives 1
print(round(1.7))   # gives 2
print(round(-1.3))  # gives -1
print(round(-1.7))  # gives -2

Floating-point real numbers can't be represented with exact precision due to hardware limitations. This can lead to cumbersome effects. See the Python docs for the details.

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print(0.1 + 0.2)  # gives 0.30000000000000004

3. math module

Python has many auxiliary functions for calculations with floats. They can be found in the math module.

To use this module, we need to import it first by writing the following instruction at the beginning of the program:

import math

For example, if we want to find a ceiling value for x - the smallest integer not less than x - we call the appropriate function from the math module: math.ceil(x). The syntax for calling functions from modules is always the same: module_name.function_name(argument_1, argument_2, ...)

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import math

x = math.ceil(4.2)
print(x)
print(math.ceil(1 + 3.8))

There's another way to use functions from modules: to import the certain functions by naming them:

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from math import ceil
 
x = 7 / 2
y = ceil(x)
print(y)

Some of the functions dealing with numbers - int(), round() and abs() (absolute value aka modulus) - are built-in and don't require any imports.

All the functions of any standard Python module are documented on the official Python website. Here's the description for math module. The description of some functions is given: