Floating Point Numbers

Floating point numbers, or floats, represent real numbers with decimal points. They are essential for calculations requiring precision, such as scientific computations, financial calculations, and more.

Characteristics of Floating Point Numbers

Precision: Floats have limited precision due to their binary representation. This can lead to small rounding errors in calculations.
Range: Floats can represent very large and very small numbers, but their precision decreases as the numbers grow larger or smaller.

Floating Point Operations

Arithmetic Operations:
- Addition: Adds two floating point numbers.
```
result = 5.5 + 3.2  # result is 8.7
```
- Subtraction: Subtracts one float from another.
```
result = 5.5 - 3.2  # result is 2.3
```
- Multiplication: Multiplies two floating point numbers.
```
result = 5.5 * 3.2  # result is 17.6
```
- Division: Divides one float by another.
```
result = 5.5 / 2.2  # result is 2.5
```
- Exponentiation: Raises one float to the power of another.
```
result = 5.5 ** 2  # result is 30.25
```
Comparison Operations:
- Equal: Checks if two floats are equal.
```
result = (5.5 == 5.5)  # result is True
```
- Not Equal: Checks if two floats are not equal.
```
result = (5.5 != 3.2)  # result is True
```
- Greater Than: Checks if one float is greater than another.
```
result = (5.5 > 3.2)  # result is True
```
- Less Than: Checks if one float is less than another.
```
result = (5.5 < 3.2)  # result is False
```
- Greater Than or Equal To: Checks if one float is greater than or equal to another.
```
result = (5.5 >= 5.5)  # result is True
```
- Less Than or Equal To: Checks if one float is less than or equal to another.
```
result = (5.5 <= 5.5)  # result is True
```

Rounding Errors

Due to the way floating point numbers are represented in binary, some numbers cannot be represented exactly, leading to rounding errors.

result = 0.1 + 0.2  # result might be 0.30000000000000004, not 0.3

Formatting Floating Point Numbers

To control the number of decimal places displayed, you can format floats using string formatting.

result = 5.6789
formatted_result = "{:.2f}".format(result)  # formatted_result is "5.68"

Type Conversion

Converting to Float: Use the float() function to convert integers or strings to a float.
```
result = float(5)       # result is 5.0
result = float("5.7")   # result is 5.7
```
Converting to Integer: Use the int() function to convert a float to an integer (truncates the decimal part).
```
result = int(5.7)  # result is 5
```