2.4. Operators and Operands

Operators are special tokens (usually symbols) that represent computations like addition and multiplication. The values the operator is applied to are called operands. For example, in the expression 5 + 10, the operator is +, and the values 5 and 10 are operands.

Python uses + and - and parentheses (for grouping) in the same way they are used in arithmetic.

Multiplication, division, and exponentiation use *, /, and **, respectively. So 3 * 4 is “three times four” and 3 ** 4 is “three raised to the fourth power” or \(3^4\).

The following code demonstrates the use of operators.

print(2 + 3) print(2 - 3) print(2 * 3) print(2 / 3) print(2 ** 3) print(3 ** 2)

When more than one operator appears in an expression, the order of evaluation depends on the rules of precedence. For mathematical operators, Python follows mathematical convention:

Parentheses, Exponentiation, Multiplication and Division, Addition and Subtraction.

Tip

When in doubt, always put parentheses in your expressions to make sure the computations are performed in the order you intend. Even if it would work correctly without them, parentheses can help you and others understand complex expressions.

2.4.1. Divison

In Python 3, the division operation always evaluates to a float, even if the result is a whole number. For example:

print(4 / 2) print(100 / 1) print(type(100 / 1))

Note

See how the values are printed with decimal points even though the decimal part is zero? That is how Python indicates a value is a float.

So for example, if we wanted to convert a number of minutes, stored in a minutes variable, into hours:

minutes = 1234 hours = minutes / 60 print(hours)

What if we just wanted to know how many whole hours are in 1234 minutes? Python provides a different division operator that can help. Integer division uses the token //. It always rounds its result down to the nearest smaller integer (moving left on the number line):

print(7 / 3) print(7 // 3) print(-7 // 3) # ! This is *not* just the negation of the previous minutes = 1234 whole_hours = minutes // 60 print(whole_hours)

2.4.2. Modulus

The modulus operator works on integers and produces the remainder when the first operand is divided by the second. In Python, the modulus operator is a percent sign %.

quotient = 7 // 3 # Integer division print(quotient) remainder = 7 % 3 # Modulus (remainder) print(remainder)

Here, 7 divided by 3 is 2 (the quotient) with 1 left over (the remainder).

The modulus operator turns out to be surprisingly useful. For example, you can check whether one number is divisible by another: if x % y is zero, then x is divisible by y. The following code finds numbers divisible by 9 (it uses a for loop and other things we’ll learn about later, but you can get an idea of how it works by reading the code and changing parts to see what happens):

for i in range(1, 100): if (i % 9) == 0: print(i, "is divisible by 9!")

You can also get the right-most digit or digits from a number using modulus. For example,``x % 10`` give you the right-most digit of x (in base 10). Similarly, x %100 gives you the last two digits of x.

for i in range(15, 25): last_digit = i % 10 print("i =", i, " last digit =", last_digit)

2.4.3. Example

Let’s say we have a number of days, and we want to know how long that is in other units of time. For example, what is 17 days in hours? What is 17 days in weeks?

Converting to hours can be done with multiplication. If we set days = 17, and then enter the code hours = days * 24 the computer would calculate our answer.

But what if we want something a bit more complicated, like converting days into weeks plus days? For example, how could we write a program where we enter days = 17 and it then tells us: 2 weeks and 3 days?

See if you can figure out how the code below uses division and modulus to get the make this conversion.

days = 123 # Convert days to hours hours = days * 24 # Convert hours to minutes minutes = hours * 60 # Convert days to *whole* weeks weeks = days // 7 # Find the remainder as remaining days remaining_days = days % 7 # Print our results print(days, "days is:") print(hours, "hours") print(minutes, "minutes") print(weeks, "weeks and", remaining_days, "days")

2.4.4. String Operations

Most of the operations that work with numbers don’t make sense when applied to strings. For example, as we’ve seen, 'Cat' / 'Dog' is an invalid expression in Python. But two of the operators above are defined for strings, though they do not perform arithmetic when applied to strings.

The + operator works with strings, but it is not addition in the mathematical sense. Instead it performs concatenation, which means joining the strings by linking them end to end. For example:

first = 10 second = 15 print(first + second) first = '100' second = '150' print(first + second)

The * operator also works with strings if applied to a string and an integer. In this case, the operation is called string repetition.

print("Hello" * 5) word = 'Test' number = 4 print(word * number)

2.4.5. Table of Operators

The following table summarizes the operators discussed above.

Operator	int, float Operation	str Operation
+	Addition	Concatenation
-	Subtraction
*	Multiplication	Repetition
/	Division
//	Integer Division
%	Modulus
**	Exponentiation