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In computing, a real number is a data type that represents numbers with a decimal point, including fractions and irrational numbers. Since computers cannot store infinitely precise numbers, real numbers are typically approximated using a finite, floating-point representation. They are used in applications like graphics, physics simulations, and artificial intelligence to represent measurements, weights, and other continuous values.

Description in computing

Floating-point numbers: The most common way to represent real numbers in computers is through floating-point data types. These use a finite number of bits to approximate real numbers, leading to potential rounding errors for numbers with infinite or very long decimal expansions.

Contrast with integers: Real numbers are distinct from integers, which are whole numbers with no fractional part.

Approximation: Due to the limits of digital storage, some real numbers cannot be stored exactly. For example, the mathematical constant pi (\(\pi \)) or the square root of 2 (\(\sqrt{2}\)) are represented as close approximations.

Applications: Real numbers are essential for many computational tasks:

Graphics and simulations: For modeling physical properties like position, velocity, and temperature.

Robotics: For path planning and precise movement control.

Artificial Intelligence (AI): To represent feature values, weights, and biases in machine learning models.

Speech and language processing: For representing data like audio spectrograms or word embeddings.