Numbers: Integers and Floats
What You'll Learn
- The difference between integers and floats
- All of Python's arithmetic operators
- Order of operations (precedence)
- Integer division and the modulo operator
- Common patterns for working with numbers
1. Integers vs. Floats
Python has two main types of numbers:
Integer (int): A whole number without a decimal point. Examples:
42, -7, 0, 1000000
Float (float): A number with a decimal point. Examples:
3.14, -0.5, 2.0, 100.0
# Integers - whole numbers student_count = 30 temperature_celsius = -5 year = 2025 # Floats - decimal numbers price = 9.99 pi = 3.14159 gpa = 3.8 # Check the type print(type(student_count)) print(type(price))
<class 'int'>
<class 'float'>
Note:
2.0 is a float, even though its value is a whole number. The presence of the decimal point makes it a float.
2. Arithmetic Operators
Python supports all the standard math operations and a few extras:
| Operator | Name | Example | Result |
|---|---|---|---|
+ | Addition | 5 + 3 | 8 |
- | Subtraction | 10 - 4 | 6 |
* | Multiplication | 6 * 7 | 42 |
/ | Division | 15 / 4 | 3.75 |
// | Integer Division | 15 // 4 | 3 |
% | Modulo (remainder) | 15 % 4 | 3 |
** | Exponentiation | 2 ** 3 | 8 |
print(5 + 3) # Addition print(10 - 4) # Subtraction print(6 * 7) # Multiplication print(15 / 4) # Division (always returns float) print(2 ** 3) # Exponentiation (2 to the power of 3)
8
6
42
3.75
8
Division always returns a float! Even
10 / 2 gives 5.0, not 5. This is an important detail in Python 3.
3. Integer Division and Modulo
Two operators deserve special attention because they are incredibly useful in programming.
Integer Division (//): Divides and rounds down to the nearest whole number (discards the remainder).
Modulo (%): Returns the remainder after division.
# Integer division: how many whole times does 4 go into 17? print(17 // 4) # 4 (4 goes into 17 four times) # Modulo: what's left over? print(17 % 4) # 1 (17 = 4*4 + 1, remainder is 1)
4
1
Practical Use: Converting Minutes to Hours
total_minutes = 135 hours = total_minutes // 60 # How many whole hours? remaining = total_minutes % 60 # How many minutes left over? print("Hours:", hours) print("Minutes:", remaining)
Hours: 2
Minutes: 15
Practical Use: Is a Number Even or Odd?
number = 42 remainder = number % 2 print(number, "divided by 2 has remainder:", remainder) # If remainder is 0, the number is even!
42 divided by 2 has remainder: 0
4. Order of Operations
Python follows the standard mathematical order of operations, sometimes remembered as PEMDAS:
- Parentheses:
()- evaluated first - Exponents:
** - Multiplication, Division, Integer Division, Modulo:
*,/,//,%(left to right) - Addition, Subtraction:
+,-(left to right)
# Without parentheses - follows PEMDAS result = 2 + 3 * 4 print(result) # 14, not 20! (multiplication first) # With parentheses - overrides default order result = (2 + 3) * 4 print(result) # 20 (parentheses first)
14
20
Temperature Conversion
# Convert Fahrenheit to Celsius fahrenheit = 98.6 celsius = (fahrenheit - 32) * 5 / 9 print("Body temp in Celsius:", celsius)
Body temp in Celsius: 37.0
The parentheses ensure subtraction happens before multiplication.
5. Mixing Integers and Floats
When you combine an integer and a float in an operation, Python automatically converts the result to a float:
print(5 + 2.0) # 7.0 (int + float = float) print(10 * 0.5) # 5.0 (int * float = float) print(7 / 2) # 3.5 (division always returns float) print(6 / 3) # 2.0 (even when it divides evenly!)
7.0
5.0
3.5
2.0
Python also provides shorthand operators for updating variables:
score = 100 score += 10 # Same as: score = score + 10 print(score) # 110 score -= 25 # Same as: score = score - 25 print(score) # 85 score *= 2 # Same as: score = score * 2 print(score) # 170
110
85
170
6. Useful Number Functions
Python has several built-in functions for working with numbers:
# abs() - absolute value print(abs(-15)) # 15 # round() - round to nearest integer or decimal places print(round(3.7)) # 4 print(round(3.14159, 2)) # 3.14 # max() and min() print(max(10, 20, 5)) # 20 print(min(10, 20, 5)) # 5
15
4
3.14
20
5
Check Your Understanding
Question 1: What is the result of 17 // 5 and 17 % 5?
17 // 5 = 3 (5 goes into 17 three whole times)
17 % 5 = 2 (17 = 5*3 + 2, the remainder is 2)
Question 2: What does 2 + 3 ** 2 * 4 evaluate to?
Answer: 38
Step by step: 3 ** 2 = 9 (exponent first), then 9 * 4 = 36, then 2 + 36 = 38.
Try It Yourself!
- Calculate the area of a rectangle with width 7.5 and height 12.3 using variables.
- Given 250 minutes, use
//and%to find how many hours and leftover minutes that is. - Use
round()to round 3.14159 to 3 decimal places.
Key Takeaways
- Integers are whole numbers; floats have decimal points.
- Python supports 7 arithmetic operators:
+,-,*,/,//,%,** - Regular division (
/) always returns a float. - Integer division (
//) discards the decimal; modulo (%) gives the remainder. - Python follows PEMDAS order of operations. Use parentheses to control the order.
- Mixing ints and floats produces a float result.