The order of operations is a set of rules that determines the sequence in which different parts of a mathematical expression are calculated. In Python, the order of operations follows the PEMDAS acronym, which stands for:
- Parentheses ( )
- Exponentiation (**)
- Multiplication (*)
- Division (/)
- Addition (+)
- Subtraction (-)
This means that any expression inside parentheses is evaluated before any other operation, followed by exponentiation, then multiplication and division (from left to right), and finally addition and subtraction (from left to right). For example, in the expression 2 + 3 * (4 - 1) ** 2, the parentheses are evaluated first, resulting in 2 + 3 * 9, then the exponentiation, resulting in 2 + 27, and finally the addition, resulting in 29.
If an expression contains multiple operators of the same precedence, such as multiplication and division, or addition and subtraction, they are evaluated from left to right. For example, in the expression 6 / 2 * 3 + 4 - 2, the division and multiplication are evaluated first, from left to right, resulting in 9 + 4 - 2, then the addition and subtraction are evaluated, from left to right, resulting in 11.
To change the order of operations, parentheses can be used to group the parts of the expression that should be evaluated first. For example, in the expression (6 / 2) * (3 + 4) - 2, the parentheses are evaluated first, resulting in 3 * 7 - 2, then the multiplication, resulting in 21 - 2, and finally the subtraction, resulting in 19.