How are floating point numbers (float) structured?

Floating point numbers (float) in Python are based on the IEEE 754 double precision standard. This is a 64-bit representation, where:

• 1 bit — sign of the number (0 — positive, 1 — negative)
• 11 bits — exponent with a bias of 1023
• 52 bits — mantissa (fractional part)

The number is calculated using the formula:

value = (-1)^sign * 1.mantissa * 2^(exponent - bias)

Where 1.mantissa is the normalized mantissa with an implicit leading one.

Due to the limited length of the mantissa and exponent, floating point numbers have finite precision and range, which can lead to rounding errors and the inability to exactly represent some decimal fractions.

In Python, the float type corresponds to C double, and for more precise calculations, the decimal module can be used.