1.5: Number Basics

Learning Objectives

By the end of this section you should be able to

• Use arithmetic operators to perform calculations.
• Explain the precedence of arithmetic operators.

Numeric data types

Python supports two basic number formats, integer and floating-point. An integer represents a whole number, and a floating-point format represents a decimal number. The format a language uses to represent data is called a data type. In addition to integer and floating-point types, programming languages typically have a string type for representing text.

Checkpoint: Integer and floating-point

Concepts in Practice \(\PageIndex{1}\): Integers, floats, and strings

Assume that x = 1, y = 2.0, and s = "32". What is the output of the following code?

print(x, type(x))

1. 1 'int'.
2. 1.0 <class 'float'>.
3. 1 <class 'int'>.

Answer

c. x = 1 is an integer, and when printing the type of an integer variable, the output is <class 'int'>.

Concepts in Practice \(\PageIndex{2}\): Integers, floats, and strings

Assume that x = 1, y = 2.0, and s = "32". What is the output of the following code?

print(y, type(y))

1. 2.0 <class 'int'>
2. 2.0 <class 'float'>
3. 2 <class 'int'>

Answer

b. y = 2.0 is floating-point number.

Concepts in Practice \(\PageIndex{3}\): Integers, floats, and strings

Assume that x = 1, y = 2.0, and s = "32". What is the type of the following value?

"12.0"

1. string
2. int
3. float

Answer

a. Any value defined within quotation marks is a string value regardless of the content.

Basic arithmetic

Arithmetic operators are used to perform mathematical operations like addition, subtraction, multiplication, and division.

Four basic arithmetic operators exist in Python:

1. Addition (+)
2. Subtraction (-)
3. Multiplication (*)
4. Division (/)

Checkpoint: Examples of arithmetic operators

Concepts in Practice \(\PageIndex{4}\): Applying arithmetic operators

Assume that x = 7, y = 20, and z = 2. Given the following lines of code, what is the output of the code?

c = 0
c = x - z
c = c + 1
print(c) 

1. 1
2. 5
3. 6

Answer

c. Line 2 of the code evaluates as follows: c = x - z = 7 - 2 = 5. Line 3 increments variable c by 1, making the total equal to 6.

Concepts in Practice \(\PageIndex{5}\): Applying arithmetic operators

Assume that x = 7, y = 20, and z = 2. What is the value of a?

a = 3.5 - 1.5

1. 2
2. 2.0
3. 2.5

Answer

b. The output of 3.5-1.5 equals 2.0 , which is a floating-point number.

Concepts in Practice \(\PageIndex{6}\): Applying arithmetic operators

Assume that x = 7, y = 20, and z = 2. What is the output of print(x / z)?

1. 3
2. 3.0
3. 3.5

Answer

c. The result of the division operation is a floating-point number that isn't rounded down. 7/2 = 3.5.

Concepts in Practice \(\PageIndex{7}\): Applying arithmetic operators

Assume that x = 7, y = 20, and z = 2. What is the output of print(y / z)?

1. 0
2. 10
3. 10.0

Answer

c. The output of the 20/2 equals 10.0 because the division operation results in a float.

Concepts in Practice \(\PageIndex{8}\): Applying arithmetic operators

Assume that x = 7, y = 20, and z = 2. What is the output of print(z * 1.5)?

1. 2
2. 3
3. 3.0

Answer

c. The output of an arithmetic operator on any floating-point operand results in a floating-point value. 2 * 1.5 = 3.0.

Operator precedence

When a calculation has multiple operators, each operator is evaluated in order of precedence. Ex: 1 + 2 * 3 is 7 because multiplication takes precedence over addition. However, (1 + 2) * 3 is 9 because parentheses take precedence over multiplication.

Table 1.4: Operator precedence from highest to lowest.

Operator	Description	Example	Result
()	Parentheses	(1 + 2) * 3	9
**	Exponentiation	2 ** 4	16
+, -	Positive, negative	-math.pi	-3.14159
*, /	Multiplication, division	2 * 3	6
+, -	Addition, subtraction	1 + 2	3

Checkpoint: Order of operations in an arithmetic expression

Concepts in Practice \(\PageIndex{9}\): Multiple arithmetic operators

What is the value of 4 * 3 ** 2 + 1?

1. 37
2. 40
3. 145

Answer

a. 3 raised to the power 2 is 9, times 4 is 36, plus 1 is 37.

Concepts in Practice \(\PageIndex{10}\): Multiple arithmetic operators

Which part of (1 + 3) ** 2 / 4 evaluates first?

1. 4 ** 2
2. 1 + 3
3. 2 / 4

Answer

b. Although addition has lower precedence than exponentiation, the parentheses cause 1 + 3 to be evaluated first.

Concepts in Practice \(\PageIndex{11}\): Multiple arithmetic operators

What is the value of -4 ** 2?

1. -16
2. 16

Answer

a. In Python, exponentiation, or raising to a power, has higher precedence than making a value negative. Python's -16 result can be confusing because, in math, "-4 squared" is 16 .

Concepts in Practice \(\PageIndex{12}\): Multiple arithmetic operators

How many operators are in the following statement?

result = -2 ** 3

1. 1
2. 2
3. 3

Answer

c. The statement uses the assignment operator (=), the negative operator (-), and the exponentiation operator (**).

Try It: Values and types

Write a Python computer program that:

1. Defines an integer variable named 'int_a' and assigns 'int_a' with the value 10.
2. Defines a floating-point variable named 'float_a' and assigns 'float_a' with the value 10.0.
3. Defines a string variable named 'string_a' and assigns 'string_a' with the string value "10".
4. Prints the value of each of the three variables along with their type.

Interactive Code

Answer

int_a = 10
float_a = 10.0
string_a = "10"

print(int_a, type(int_a))
print(float_a, type(float_a))
print(string_a, type(string_a))

Try It: Meters to feet

Write a Python computer program that:

1. Assigns the integer value 10 to a variable, meters.
2. Assigns the floating-point value 3.28 to a variable, meter2feet.
3. Calculates 10 meters in feet by multiplying meter by meter2feet. Store the result in a variable, feet.
4. Prints the content of variable feet in the output.

Interactive Code

Answer

meters = 10
meter2feet = 3.28
feet = meters * meter2feet
print(feet)