Python: Numbers

Python Numbers

python
numbers
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Author

pedromartinezduran

Published

Sunday, June 1, 2025

Modified

Saturday, October 4, 2025

1 Overview

📘 Numbers in Python

Python has built-in support for numbers, including integers, floating-point numbers, and complex numbers. This module focuses on working with numeric data types and operations in Python, covering everything from basic arithmetic to more advanced mathematical functions.

2 Numbers

  • Numbers are a “simple” way to describe the world:

    • How many apples you sold.
    • How much money you earned.
    • How many minutes are in a year.
    • Even a picture on your phone — it’s just millions of numbers for colors.

3 Numbers

  • So when we teach computers to work with numbers, we’re giving them the building blocks to represent reality.

  • Once we have numbers, we can automate represent and manipulate anything algebraic: sales, costs, scores, time, even images and music.

4 Supermarket Scale Cost

  • Automate cost calculation in a supermarket scale.
  • The same code can be reused every day by changing the variables.
apple_kgs = 1.5
apple_price_kg = 2

cost = apple_kgs * apple_price_kg

print("Cost:", cost, "e")
Cost: 3e

5 Tomato Stall

  • Automate net income (before IRPF) calculation in a market’s day.
tomatoes_kg_sold = 30
price_per_kg = 1.5

production_costs_day = 0.5  # Daily cost for water, fertilizer, pesticides...
stall_rent_per_day = 20
social_security_day = 200 / 30
iva = 0.1  # %

daily_revenue = tomatoes_kg_sold * price_per_kg
expenses = production_costs_day + stall_rent_per_day + social_security_day
income = daily_revenue - expenses
net_b4_irpf = income / (1 + iva)

print("Today's net (before IRPF):", net_b4_irpf, "e")
Today’s net (before IRPF): 16.21e

6 Numbers in Python

  • int (integers)
  • float (floating-point)
  • Decimal
  • Complex

7 Integers

Whole numbers without decimal points:

  • positive
  • negative
  • zero
print(type(4))
print(type(0))
print(type(-145))
<class ‘int’>
<class ‘int’>
<class ‘int’>

Basic integer operations: addition, subtraction, multiplication, floor division, modulus, and exponentiation.

x = 10
y = 3

print(x + y)  # addition
13 
print(x - y)  # subtraction
7 
print(x * y)  # multiplications
30

  • Integer division (or floor division) rounds down the result to the nearest whole number.

    print(x // y) # floor division
    3 
print(x % y)  # modulus
1

  • In other languages, a common operator for exponentiation is ^, but this is not the case in Python!

    print(x ** y) # exponentiation
    1000

8 Floats

Numbers with decimal points (floating-point numbers).

x = 4.5
y = 2.61

print(x + y)  # addition
7.109999999999999 
print(x - y)  # subtraction
1.8900000000000001 
print(x * y)  # multiplications
11.745 
print(x / y)  # division
1.7241379310344829 
print(x % y)  # modulus
1.8900000000000001 
print(x ** y) # exponentiation
50.68560805900789
  • Limitations due to the way computers represent decimal numbers.
  • Ints and floats can be mixed, giving the most restrictive type as a result:
x = 1   # this is an integer
y = 2.8 # this is a float
z = x + y

print(z, type(z))
3.8 <class ‘float’>
  • There can be rounding errors:
# This result should be 0.3
print(0.1 + 0.2)
0.30000000000000004

9 Round

  • round() function rounds to the nearest whole number.
print(round(2.4))
2 
print(round(2.6))
3
  • If specified, rounds to a specific number of decimal places.
# Round to 2 decimal places
print(round(0.123456, 2))
0.12 
# Round to 5 decimal places
print(round(0.123456, 5))
0.12346

10 Underscore

  • Underscores _ can be used as visual separator in numbers.
  • Improves readability of big numbers.
  • Has no impact on the value of the number.
# Using underscores in integers for better readability
one_million = 1_000_000
one_billion = 1_000_000_000

# Compare it without underscores, it is much more difficult to read
one_million = 1000000
one_billion = 1000000000

11 Type conversion

  • int to float:
x = 10
print(type(x))
<class ‘int’> 
# Convert to float
x = float(x)
print(x, type(x))
10.0 <class ‘float’>
  • float to int:
x = 4.6
print(type(x))
<class ‘float’> 
# Converting to int truncates the decimals
x = int(x)
print(x, type(x))
4 <class ‘int’>

12 Operation precedence

  • ()

    <!– * **

  • -x –>

  • *, /, //, % (same precedence, evaluated from left to right)

  • +, - (same precedence, evaluated from left to right)

result = 2 + 3 * 4 - 1
print(result)

  • Result?

result = (2 + 3) * (4 - 1)
print(result)

  • Result?

13 Booleans

  • Data type for representing true and false statements.
is_true = True
is_false = False

Conversion to bool:

  • bool(0) → False (True for any number different than 0).

  • bool('') → False (True for any other string).

  • Internally, True is the integer 1 and False the integer 0.
print(True + 3)  # True is treated as 1, so the result is 1 + 3 = 4
4 
print(False * 5)  # False is treated as 0, so the result is 0 * 5 = 0
0

14 Logical operators

  • Used for manipulating boolean values.
  • Python keywords: and, or, not.

15 and

  • Is true when all the elements are true, and false otherwise.
True and True   # True
True and False  # False
False and True  # False
False and False # False

16 or

  • Is false when all the elements are false, and true otherwise.
True or True   # True
True or False  # True
False or True  # True
False or False # False

17 not

  • Negates the element.
not True  # False
not False # True
  • We can chain as many as we want:
True and True and True and True # True
True and True and True and False # False

True or True or True or False # True
False or False or False or False # False

(True and True) or (True and False) # True

18 Precedence

  • Logical operators have lower precedence than arithmetic operators.

  • The precedence, highest to lowest:

    • not
    • and
    • or

  • Logical operators have lower precedence than arithmetic operators.

  • The precedence, highest to lowest:

    • not
    • and
    • or

  • Is the following expression true or false?

False or True and not True

print(False or True and not True)
False
  • The expression above is evaluated as if written like:

False or (True and (not True))

19 Comparison operators

Evaluate relationship between values or expressions with True or False.

  • Equal to (==)

  • Not equal to (!=)

  • Less than (<)

  • Greater than (>)

  • Less than or equal to (<=)

  • Greater than or equal to (>=)

# Equal to

5 == 5  # True
5 == 6  # False
# Not equal to

5 != 5  # False
5 != 6  # True
# Less than

5 < 6  # True
6 < 5  # False
# Greater than

5 > 6  # False
6 > 5  # True
# Less than or equal to

5 <= 5  # True
5 <= 6  # True
6 <= 5  # False
# Greater than or equal to

5 >= 5  # True
6 >= 5  # True
5 >= 6  # False
  • Comparison operators can be combined with logical operators:
x = 5
y = 7

print(x < y and y < 10)
True
  • They can be chained with no limit:
print(3 < 5 < 7)  # Equivalent to (3 < x) and (x < 7)
True 
## Comparison operators precedence
# - Higher precedence than logical operators (`not`, `and`, `or`).
# - Lower precedence than arithmetic operators.
# 
# 3 < 5 * 2  # equivalent to 3 < (5 * 2)
# 3 < 5 and 5 < 7  # equivalent to (3 < 5) and (5 < 7)

20 Built-in functions

# absolute value
print(abs(-2))
2 
# two to the power of 3
print(pow(2, 3))
8.0 
# returns the minimum number
print(min(2, 1, 4, 9, 5))
1 
# returns the maximum number
print(max(2, 1, 4, 9, 5))
9

21 Imports

  • Used to bring external code into your current program.
import math
# Calculate square root
print(math.sqrt(9))
3.0 
# Show pi
print(math.pi)
3.141592653589793 
# Example of importing a single function from a module:
# from math import sqrt
# print(sqrt(9))

# Example of importing multiple functions:
# from math import sqrt, pi
# print(sqrt(9))
# print(pi)

# Example of importing all functions (not recommended):
# from math import *
# print(sqrt(9))
# print(pi)

# Example of importing with aliases:
# import math as m
# print(m.sqrt(9))
# 
# from math import sqrt as square_root
# print(square_root(9))

  • Python Standard Library: math, random, statistics, etc.

  • random example:

import random

# Generates a random integer between 1 and 10
random_number = random.randint(1, 10)
print(random_number)
7

22 Example

Write a program in which the user enters his/her weight (in kg) and height (in m). The system then calculates the Body Mass Index as weight divided by height squared.

# Calculate BMI

weight = float(input("Enter your weight in kilograms:"))
height = float(input("Enter your height in meters:"))

bmi = weight / height ** 2
print("Your BMI is", bmi)

23 Code readability

  • Essential for making your code easier to understand and maintain.
  • Start practicing with good coding as soon as possible.
  • First tips:
    • Choose meaningful variable names. E.g. user_name.
    • Use white spaces effectively. E.g. x = x + 1 (instead of x=x+1).
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