float — Floating-Point Data Type

Visual reference

What you will learn

• What is float? — store real numbers with decimal places
• Type promotion — why int + float becomes float
• Scientific notation — 3e2, 100e-2, 5e-66
• Important rule — binary, octal, and hex float literals are invalid

Big picture: where does float fit?

In the previous lesson, int stored whole numbers. float stores real numbers — values with a fractional (decimal) part.

Key idea: both are numeric types, but float can represent fractions while int cannot.

What is a floating-point number?

float is a pre-defined class and a fundamental type.

Purpose: store real constant values — numbers with decimal places — such as percentages, CGPA, commission, or DA amounts.

Valid floats	Not floats
12.34, 0.5, -7.25, 3e8	10, 100, 0b101 (those are int)

Analogy

• int counts apples → 5 apples
• float measures weight → 5.75 kg

A weighing scale needs decimals, so it uses floating-point values.

Creating a float

Assign a value with a decimal point (or use scientific notation).

price = 12.34

print(price)
print(type(price))

12.34
<class 'float'>

Python sees the decimal point and stores the value as float.

Why does 10 + 1.2 become a float?

Type promotion: if any operand is a float, Python promotes the result to float so you do not lose the fractional part.

a = 10      # int
b = 1.2     # float
c = a + b

print(c)
print(type(c))

11.2
<class 'float'>

Interactive: type promotion

Use the playground at the bottom of this page. Change a and b in the starter code, run again, and check type(c).

Division always returns a float

Even when both operands are int, / produces a float because the answer can have a fractional part.

print(22 / 7)

3.142857142857143

Compare the two division operators:

Expression	Result	Type
22 / 7	3.142857...	float
22 // 7	3	int

• / — floating-point division
• // — integer (floor) division

Scientific notation (exponent form)

General form: mantissa e exponent → value = mantissa × 10exponent.

Advantage: compact storage for very large or very small values (your notes: minimizes memory for big floating-point values).

a = 3e2
b = 100e-2

print(a)
print(b)

300.0
1.0

Try these mentally, then verify in the playground:

Expression	Meaning	Value
3e2	3 × 10²	300.0
5e3	5 × 10³	5000.0
8e-2	8 × 10⁻²	0.08
1.5e3	1.5 × 10³	1500.0

Change the exponent in expressions like 3e2 in the playground to explore scientific notation interactively.

Why computers use scientific notation

Storing this literal is awkward:

0.000000000000000000000000000000000000000000000000000000000000000005

Python displays it compactly:

a = 0.000000000000000000000000000000000000000000000000000000000000000005
print(a)

5e-66

Common in physics, finance, and machine learning.

Important rule: only decimal float literals

Valid:

10.5
0.25
3e8

Not valid (from your notes):

# 0b1010.0b1111   # SyntaxError: invalid decimal literal
# 0o23.0b1010
# 0xAC.0o23

Binary, octal, and hexadecimal prefixes belong to int literals. Convert when you need a float:

x = float(0b1010)
print(x)

10.0

Real-world applications

CGPA — 8.67

Percentage — 12.5%

Weight — 72.35 kg

Scientific data — 5e-9

Memory tip: int vs float

Use int when…	Use float when…
Counting students	Measuring height
Employee ID	Salary percentage
Number of products	Temperature
Age (whole years)	Scientific measurements

Rule of thumb: if the value can have a fractional part, choose float.

Practice exercises

Exercise 1 — store your height as a float:

height = 172.5
print(height, type(height))

Exercise 2 — predict, then run:

print(1 / 3)

Answer: 0.3333333333333333

Exercise 3 — predict, then run:

print(1.5e3)

Answer: 1500.0

Quick knowledge check

1. Why is 10 + 1.2 a float?
   One operand is already float; Python promotes the result.

2. What does 3e2 mean?
   3 × 10² = 300.0.

3. Is 0b101.1 a valid float literal?
   No — only decimal-style float literals; 0b is for integers.

Summary

• float stores real numbers with decimal places or scientific notation.
• Type promotion: int + float → float.
• / returns float; // returns int.
• Scientific notation (e) compactly represents huge and tiny values.
• 0b / 0o / 0x cannot be used as float literals — use float(...) on an integer instead.

Next lesson: bool — Boolean data type (True, False, and logical values).