Contents

• Overview
• Precision
• Mathematical Operations
• Combining Operations
• Order of Operations
• Parenthses

Overview

An integer in the context of programming and mathematics is a whole number (sometimes called a counting number) that can be positive, negative, or zero, but it does not include any fractional or decimal parts. In programming languages like Python, an integer is a fundamental data type that is used to represent these whole numbers. Integers are used extensively in various types of calculations and loops, as well as in indexing and more complex mathematical operations. I

In most programming languages, integers have a certain range of values they can represent, determined by the number of bits allocated for storing them in memory. In Python, however, integers have unlimited precision, meaning they can grow to have as many digits as needed, limited only by the available memory. This is a significant benefit of Python, this means we can specify an integer of (virtually) any length.

Examples of Integers in Python:

• 10
• 157
• 24785
• 12234987923847928374982739847928374687693589056890347

In Python, we can perform mathematical calculations using Integers using operators which are symbols to represent valid arithmatic operations for integer values. Here are the first of these that we will explore:

print(10 + 20)
print(10 + 20 + 30)
print(10 + 20 + 30 + 40 + 50 + 60)

print(20 - 10)
print(30 - 20 - 10)
print(10 - 20)
print(10 - 20 - 30)

print(10 * 20)
print(10 * 20 * 30)
print(10 * 20 * 30 * 40 * 50 * 60)

print(10 / 2)  # Note the result is an int
print(10 / 3)  # Note the result is a float (int part and decimal part)
print(10 / 0)  # Note that this example produces an error as the divisor cannot be zero because division by zero is undefined.

print(10 // 2)  # Note the result is an int
print(10 // 3)  # Note the result is an int, the decimal part was discarded

print(10 % 2)  # Note the result is zero because there is no remainder after the division
print(10 % 3)  # Note the result is 1 because there is a remainder after the division

print(10 ** 2)
print(10 ** 3)
print(10 ** 100)

Any of the mathematical operators can be used in more complex (combined) mathematical calculations. Here are some examples:

print(10 + 20 - 15 * 5)
print(10 + (100 / 2))  # See the note about the use of parenthses below
print(10 ** (2 * 30)))  # See the note about the use of parenthses below

In Python, the order of operations for mathematical operators follows the conventional mathematical hierarchy, which is consistent with the rules of arithmetic that are typically taught in mathematics (often remembered by the acronym PEMDAS/BODMAS). For the operators you've listed (+, -, *, /, //, %, and **), the order of precedence is as follows:

• Exponents (**)
• Multiplication (*) and Division (/, //, and %)
• Addition (+) and Subtraction (-)

In Python, like math, we can use parenthses ( ) to isolate and group factors of our equations to override andn control the order of operations. See the examples in the Combining Operations section above.