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The expression "frac(1/√2)" refers to the fractional part of the reciprocal of the square root of 2, a common irrational number approximately equal to 1.414213562. The square root of 2, denoted as √2, is the positive real number that, when multiplied by itself, yields 2. It is an irrational number, meaning its decimal representation is non-terminating and non-repeating.

The reciprocal of √2 is calculated as 1/√2, which simplifies to √2/2 when rationalized by multiplying the numerator and denominator by √2. This results in the value approximately equal to 0.707106781. The term "frac(1/√2)" specifically denotes the fractional part of this value, which is the number minus its integer component. Since 1/√2 is already less than 1, its fractional part is simply the number itself, approximately 0.707106781.

In mathematics, the fractional part of a real number x is often denoted as {x} and is defined as x minus the greatest integer less than or equal to x. For 1/√2, since it lies between 0 and 1, its fractional part is identical to its value. This concept is useful in various areas of analysis, number theory, and applied mathematics, particularly in studying periodic behavior and modular arithmetic.

The exact value of 1/√2 can be expressed in different forms, such as √2/2 or (2^(1/2))^(-1), and it appears in contexts like trigonometric identities, complex numbers, and geometric constructions. Its fractional part remains the same regardless of representation, as it is inherently tied to the number's position on the real number line.