Back to Basics - Python #02

The Numeric data type

There are eight major data types in Python:

Numeric data types are widely used in mathematical, statistical, data science, and machine learning solutions.

There are three distinct numeric types in Python:

• int (integer)
• float
• Complex

Integers

What is an integer?

An integer is a whole number, positive or negative, with no fractional part, i.e., no decimals, and unlimited length. It includes the 0 (zero).

We can write them down as "...-3, -2, -1, 0, 1, 2, 3..."

Python uses the class int to represent all integer numbers.

When we define a variable num with a value of 5, the variable num does not hold the real integer 5. It stores a reference pointing to where the integer 5 is held in the computer's memory.

num = y
print(type(num))  # returns the variable num's type

The output is:

<class 'int'>

Note: In Python 3, there is effectively no limit to how long an integer value can be. The limit is constrained by the amount of memory your system has.

Integer operations

We can perform all standard mathematical operations using Python's integers, including:

For example:

num_1 = 10
num_2 = 5

c = num_1 + num_2
print(c)
print(type(c))

c = num_1 - num_2
print(c)
print(type(c))

c = num_1 * num_2
print(c)
print(type(c))

c = num_1 / num_2
print(c)
print(type(c))

c = num_1 ** num_2
print(c)
print(type(c))

The above calculations will return the following:

# Addition
15
<class 'int'>

# Subtraction
5
<class 'int'>

# Multiplication
50
<class 'int'>

# Division
# Note the result of the division is a decimal number. 
# More on that later.
2.0
<class 'float'>

# Exponetiation
100000
<class 'int'>

Floats

In addition to integers, consisting of whole numbers without fractions, Python also offers us the float type.

What is a float number?

A float is a positive or negative number with afractional part, i.e., decimals, and unlimited length. It includes the 0 (zero).

Float numbers precision

Python’s built-in float data type provides up to 15 digits of decimal precision. That is usually enough for common calculations.

100 / 30
3.3333333333333335 
# The floor division above returns a float.
# Note the value is rounded to the nearest 15-digit value available.

The default precision is 6 decimal places. You can set the precision using the round():

For example:

x = 7.78
y = 3.3
result = x * y  # return 25.674
round(result, 2) 
25.67   # returns 'result' round to two decimals

Operations with Floats

Operations with floats follow the same rules as operations with integers. The difference is, for obvious reasons, the presence of decimal points in the numbers used for the calculations.

Order of Operations

As in normal mathematical calculations, Python integers and floats follow a defined order when performing operations. The famous PEMDAS:

PEMBAS

PEMDAS was created to help remember the mathematical order of operations.

PEMBAS Rank and Priority

* In PEMDAS Multiplication and Division have equal rank in the order of operations and do not need to be in any specific order. Whichever comes first, from left to right, is performed first.

** The same principle of equal ranking applies to Addition and Subtraction. Whichever comes first, from left to right, is performed first.

Examples:

# Here multiplication happens first then the division
6 * 2 / 4
3.0

# And here the Division takes place first the the multiplication
6 / 2 * 4
12.0

Division and Floor Division

In Python, there are two ways to divide numbers:

• The normal division using the / operator;
• and the floor division, using the // operator.

Which one we will use will depend on the result we want to achieve.

What is the difference between the two?

The single forward slash operator / is known as float division and always returns a float point value.

We would normally expect the following when performing a float division.

# Two integers
100 / 30
3.3333333333333335

# One float and an integer
100.0 / 30
3.3333333333333335

# Two floats
100.0 / 30.0
3.3333333333333335

The double forward slash operator // returns a floored integer or a floating point value.

The result of a double slash operator will depend on whether we use int or float numbers.

Examples:

# Two integers return an integer. Where it is an exact division, 
# and there is no remainder.
100 // 25
4

# One integer and a float, always return a float.
100 // 25.0
4.0

# Two floats always return a float.
100.0 // 25.0
4.0

One interesting note about this is what happens with negative numbers:

-7.0 // 3
-3.0

This makes sense because the result will be rounded down (i.e., floored), meaning that while we may expect it to be equal to -2.0, rounded down, the value is correctly -3.0.

Complex Numbers

Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and ‘i’ is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

Examples of complex numbers:

x = 7 + 2i
y = -5 + 1.2i

Conversion between Numeric types

A Numeric type can be converted into another numeric type by typecasting with the intended type.

x = 2.78
int_x = int(x)  # converts a float into an integer

y = 4
float_y = float(y)  # converts an integer into a float

Important notes on conversions:

• Converting a float to an integer will truncate the decimal part. In the example above, converting 2.78 into an integer, the result was 2, the number before the decimal point. Turning 2.99 into an int would still return 2.
• Converting a large integer to float may lose precision.
• Converting an integer to a complex number just adds 0j as the imaginary part.

The use of Numeric types

There are numeric types all over the programming world. Some examples of areas where Numeric types are used but not restricted to:

• Finance apps
• Games
• Scientific apps
• Statistics
• Graphics
• Machine Learning
• Web Development
• Data Analysis and Data Science
• Embedded systems

Summary

Whether using Python for programming, analysis, or web development, amongst other fields, developers rely heavily on Numeric types. Integers, float, complex numbers, calculations, equations, designing; the possibilities are endless.

Understanding how Numeric types work is an essential and useful skill people should have. It becomes even more important if our fields of work involve working with programming languages. Fortunately, Python is a solid language for processing numbers and has a very generous number of libraries available to expand Python's capability even further.

Have a go at exploring Python Numeric types. It will certainly be a nice addition to your programming skills. Pun intended.