2.5 Dividing integers

Division in Python offers versatile tools for various calculations. True division gives precise results with decimals, while floor division and modulo handle whole number operations and remainders.

These operators are crucial for unit conversions, checking even/odd numbers, and solving math problems. Understanding their differences and applications enhances your ability to manipulate numbers effectively in Python programming.

Division and Modulo in Python

True vs floor division

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• True division uses the

  /

  operator returns a floating-point number (3.5) while floor division uses the

  [//](https://www.fiveableKeyTerm://)

  operator returns the largest integer less than or equal to the division result also known as integer division (3)
• True division always returns a float, while floor division returns an integer rounds down to the nearest integer
• Floor division is an example of integer arithmetic, where the result is always an integer

Modulo for remainders and conversions

• Modulo operator uses the

  [%](https://www.fiveableKeyTerm:%)

  symbol returns the remainder of a division operation (7 % 2 = 1)
• Modulo is useful for finding the remainder of a division operation to check if a number is even or odd, use

  number % 2

  • If the result is 0, the number is even
  • If the result is 1, the number is odd
• Modulo can be used to extract the remaining units after division when converting 65 minutes to hours and minutes

  1. 65 // 60 = 1

     hour

  2. 65 % 60 = 5

     minutes
  • 65 minutes is equal to 1 hour and 5 minutes

Floor division with modulo

• Combining floor division and modulo allows for separating the whole units and remaining units in various unit conversion scenarios
  • Floor division returns the whole number of units
  • Modulo returns the remaining units
• When converting 150 seconds to minutes and seconds

  1. 150 // 60 = 2

     minutes (floor division)

  2. 150 % 60 = 30

     seconds (modulo)
  • 150 seconds is equal to 2 minutes and 30 seconds
• Converting 1000 centimeters to meters and centimeters

  1. 1000 // 100 = 10

     meters (floor division)

  2. 1000 % 100 = 0

     centimeters (modulo)
  • 1000 centimeters is equal to 10 meters and 0 centimeters

Arithmetic Operators and Operands in Division

• Division operations use arithmetic operators (such as /, //, and %) to perform calculations on operands
• In a division operation, the number being divided is called the dividend, while the number it's being divided by is the divisor
• Rounding in division can be achieved through floor division or by using specific Python functions

Number Theory and Integer Division

• Integer division is a fundamental concept in number theory, dealing with the properties and relationships of integers
• The modulo operation is particularly useful in number theory for studying divisibility and finding patterns in sequences of numbers