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Lesson 06 - Numbers (Integers and Float)

Python uses integers and floats to handle numbers. Learn the difference and see how it affects real architectural calculations like areas, heights, and budgets.

Introduction

Architects work with numbers constantly. Floor counts, room areas, building heights, budget calculations.

Python handles numbers in two ways: integers (whole numbers) and floats (decimal numbers).

Understanding the difference matters. It affects how your calculations work and what results you get.

This lesson shows you how Python treats numbers and how to use them in real architectural calculations.

Lesson Overview

This section contains a general overview of topics you will learn in this lesson.

  • Understand the difference between integers and floats
  • Learn when to use each type
  • Perform basic math operations (+, -, *, /)
  • Understand why division behaves differently than you expect
  • See how number types affect real calculations

Two Types of Numbers

Python treats whole numbers and decimal numbers as different types.

Integers (int) — Whole numbers, no decimal point

floor_count = 12
window_count = 48
door_count = 24

Floats (float) — Numbers with decimal points

floor_height = 3.2
room_area = 42.5
wall_thickness = 0.2

When to Use Each Type

Use Integers When Counting Things

Things you count are always whole numbers. You can't have 12.5 floors or 3.7 doors.

# Counting
floor_count = 8
room_count = 45
column_count = 16

# IDs and numbers
sheet_number = 101
revision_number = 3

Use Floats When Measuring Things

Measurements are rarely exact whole numbers.

# Distances and heights
floor_height = 3.2
ceiling_height = 2.7
wall_length = 12.5

# Areas and volumes
room_area = 42.5
floor_area = 850.75

# Coordinates
x_coordinate = 125.3
y_coordinate = 78.9

Basic Math Operations

Python uses the operators you already know.

Addition (+)

ground_floor_height = 4.5
typical_floor_height = 3.2
total_height = ground_floor_height + typical_floor_height

print(total_height)  # Output: 7.7

Subtraction (-)

total_area = 450.0
circulation_area = 75.5
usable_area = total_area - circulation_area

print(usable_area)  # Output: 374.5

Multiplication (*)

floor_count = 8
floor_height = 3.2
total_height = floor_count * floor_height

print(total_height)  # Output: 25.6

Division (/)

total_area = 450.0
floor_count = 3
area_per_floor = total_area / floor_count

print(area_per_floor)  # Output: 150.0

The Division Surprise

Division in Python always returns a float, even when dividing whole numbers.

total_floors = 12
half_floors = total_floors / 2

print(half_floors)    # Output: 6.0 (not 6)
print(type(half_floors))  # Output: <class 'float'>

Notice: 6.0 not 6. The result is a float.

This is intentional. Python assumes you want precision.

Integer Division (//)

If you want to divide and get an integer back, use // (floor division).

total_floors = 13
floors_per_section = total_floors // 3

print(floors_per_section)  # Output: 4 (not 4.333...)

Floor division divides and rounds down to the nearest whole number.

When This Matters

# You have 100 seats and tables that fit 8 people
seats = 100
seats_per_table = 8

tables_needed = seats // seats_per_table
print(tables_needed)  # Output: 12

# Regular division would give you 12.5 tables
# But you can't have half a table

Modulo (%) — The Remainder

The modulo operator % gives you the remainder after division.

seats = 100
seats_per_table = 8

tables_needed = seats // seats_per_table
leftover_seats = seats % seats_per_table

print(tables_needed)    # Output: 12
print(leftover_seats)   # Output: 4

You need 12 tables. 4 seats will be left over.

Architectural Use Case

# You're ordering tiles. Tiles come in boxes of 25.
tiles_needed = 378
tiles_per_box = 25

boxes_needed = tiles_needed // tiles_per_box
extra_tiles = tiles_needed % tiles_per_box

print(boxes_needed)  # Output: 15 boxes
print(extra_tiles)   # Output: 3 tiles short

# You need 16 boxes to have enough

Exponentiation (**)

Raise a number to a power using **.

# Area of a square
side_length = 5
area = side_length ** 2

print(area)  # Output: 25

# Volume of a cube
side_length = 3
volume = side_length ** 3

print(volume)  # Output: 27

Mixing Integers and Floats

When you mix integers and floats, Python converts the result to a float.

floor_count = 8        # Integer
floor_height = 3.2     # Float

total_height = floor_count * floor_height
print(total_height)    # Output: 25.6 (float)

This is called type promotion. Python promotes the integer to a float to avoid losing precision.

Order of Operations (PEMDAS)

Python follows standard math rules.

Parentheses

Exponents

Multiplication and Division (left to right)

Addition and Subtraction (left to right)

# Without parentheses
result = 10 + 5 * 2
print(result)  # Output: 20 (multiplication first)

# With parentheses
result = (10 + 5) * 2
print(result)  # Output: 30 (parentheses first)

Architectural Example

# Calculate total building height
ground_floor_height = 4.5
typical_floor_height = 3.2
floor_count = 8

# Wrong (without parentheses)
total_height = ground_floor_height + floor_count * typical_floor_height
print(total_height)  # Output: 30.1
# This calculates: 4.5 + (8 * 3.2) = 4.5 + 25.6

# Correct (with parentheses)
typical_floors = floor_count - 1
total_height = ground_floor_height + (typical_floors * typical_floor_height)
print(total_height)  # Output: 27.9
# This calculates: 4.5 + (7 * 3.2) = 4.5 + 22.4

When in doubt, use parentheses. They make your intent clear.

Real Architectural Calculations

Example 1: Building Height

ground_floor_height = 4.5
typical_floor_height = 3.2
floor_count = 12

# Ground floor + typical floors
typical_floors = floor_count - 1
total_height = ground_floor_height + (typical_floors * typical_floor_height)

print("Building height:", total_height, "meters")
# Output: Building height: 39.7 meters

Example 2: Floor Area Ratio (FAR)

site_area = 2000.0
gross_floor_area = 8500.0

far = gross_floor_area / site_area

print("Floor Area Ratio:", far)
# Output: Floor Area Ratio: 4.25

Example 3: Budget Per Square Meter

total_budget = 5000000
total_area = 3500.0

cost_per_sqm = total_budget / total_area

print("Cost per sqm:", cost_per_sqm)
# Output: Cost per sqm: 1428.5714285714287

Notice: The result has many decimal places. We'll learn to format numbers properly in a later lesson.

The Pain vs The Python Fix

The Pain: Calculating building metrics by hand. Every time a dimension changes, you recalculate everything.

The Python Fix: Define the variables once. Change one value, everything updates.

# Define once
floor_count = 12
floor_height = 3.2
ground_floor_height = 4.5

# Calculate automatically
typical_floors_height = (floor_count - 1) * floor_height
total_height = ground_floor_height + typical_floors_height
average_height = total_height / floor_count

print("Total height:", total_height)
print("Average height:", average_height)

# Change floor count
floor_count = 15

# Recalculate automatically
typical_floors_height = (floor_count - 1) * floor_height
total_height = ground_floor_height + typical_floors_height
average_height = total_height / floor_count

print("New total height:", total_height)
print("New average height:", average_height)

Common Mistakes

Mistake 1: Expecting integer division to give an integer

total_floors = 12
result = total_floors / 2

print(result)  # Output: 6.0 (float, not 6)

Use // if you want an integer.

total_floors = 12
result = total_floors // 2

print(result)  # Output: 6 (integer)

Mistake 2: Dividing by zero

area = 450.0
floor_count = 0

area_per_floor = area / floor_count
# Error: ZeroDivisionError: division by zero

Python can't divide by zero. Check your values before dividing.

Mistake 3: Forgetting order of operations

# You want: 4.5 + (7 * 3.2)
# You write:
total = 4.5 + 7 * 3.2
print(total)  # Output: 26.9 (correct, but unclear)

# Better (explicit):
total = 4.5 + (7 * 3.2)
print(total)  # Output: 26.9 (clear intent)

Mistake 4: Confusing * (exponent) with ^ (not exponent in Python)

# Wrong (^ is not exponent in Python)
area = 5 ^ 2  # This does something else entirely

# Correct
area = 5 ** 2
print(area)  # Output: 25

Assignment

  1. Create a new file called building_calculations.py
  2. Define these variables:
    • Ground floor height (4.5 meters)
    • Typical floor height (3.2 meters)
    • Number of floors (10)
    • Site area (1500 square meters)
    • Floor area per level (450 square meters)
  3. Calculate and print:
    • Total building height
    • Total gross floor area
    • Floor Area Ratio (FAR)
    • Average floor height
  4. Change the number of floors to 15 and run the script again. Verify all calculations update.
  5. Experiment:
    • Try dividing by zero. Read the error.
    • Calculate the number of full floors in 32 meters with 3.2m floor height (use //)
    • Find how many meters are left over (use %)
    • Calculate the area of a square room with 4.5m sides (use *)
  6. Create a budget calculation:
    • Total budget: 4,000,000
    • Total area: 2,800 square meters
    • Calculate cost per square meter
    • Calculate 15% contingency on the budget

Knowledge Check

The following questions are an opportunity to reflect on key topics in this lesson.

Additional Resources

This section contains helpful links to related content. It isn't required, so consider it supplemental.

Updated on Mar 27, 2026