float Fundamentals¶

The float type represents floating-point numbers, which are numbers with fractional parts.

Examples:

3.14
0.5
-2.75
1.0
````

Floats are used to represent:

* measurements
* scientific values
* real-number approximations
* division results

```mermaid
flowchart TD
    A[float]
    A --> B[whole part]
    A --> C[fractional part]

1. Floating-Point Numbers¶

A floating-point number usually includes a decimal point.

x = 3.14
y = -0.25
z = 2.0

Unlike integers, floats can represent values between whole numbers.

2. Float Arithmetic¶

Floats support the same main arithmetic operators as integers.

a = 5.5
b = 2.0

print(a + b)
print(a - b)
print(a * b)
print(a / b)

Output:

7.5
3.5
11.0
2.75

3. Division Produces Floats¶

In Python, the / operator returns a float even when the mathematical result is a whole number.

print(6 / 2)

Output:

3.0

This behavior distinguishes / from floor division //.

4. Scientific Notation¶

Python supports scientific notation for floats.

a = 1.5e3
b = 2.0e-2

print(a)
print(b)

Output:

1500.0
0.02

This notation is useful in science and engineering.

5. Floating-Point Approximation¶

Floats are approximations, not exact representations of most decimal fractions.

For example:

print(0.1 + 0.2)

Output may be:

0.30000000000000004

This happens because many decimal values cannot be represented exactly in binary floating-point form.

flowchart LR
    A[decimal value] --> B[binary approximation] --> C[stored float]

6. Comparing Floats Carefully¶

Because floats are approximate, direct equality comparisons can be misleading.

print(0.1 + 0.2 == 0.3)

Output:

False

A safer approach is to compare with tolerance.

x = 0.1 + 0.2
print(abs(x - 0.3) < 1e-9)

Output:

True

7. Converting to Float¶

The float() function converts compatible values to floats.

print(float(5))
print(float("3.14"))

Output:

5.0
3.14

8. Worked Examples¶

Example 1: average¶

total = 7
count = 2
average = total / count

print(average)

Output:

3.5

Example 2: measurement¶

length = 2.5
width = 4.0
area = length * width

print(area)

Output:

10.0

Example 3: approximation issue¶

x = 0.1 + 0.2
print(x)

9. Common Pitfalls¶

Expecting exact decimal behavior¶

Floats are not ideal when exact decimal arithmetic is required, such as in financial calculations.

Comparing with ==¶

Direct equality is often unsafe for computed float values.

10. Summary¶

Key ideas:

• float represents numbers with fractional parts
• floats support ordinary arithmetic
• division with / produces floats
• floating-point values are approximations
• float comparisons often require tolerance

The float type is essential for measurements, ratios, and scientific computation.