316227766

316,227,766 is a positive integer of nine digits. It equals 2 × 158,113,883 and is approximately 3.16227766 × 10^8. In decimal form, it appears as the integer part of a scaled irrational constant rather than a value defined by a simple ratio.

Mathematical significance: This number is the floor of sqrt(10^17), since sqrt(10^17) ≈ 316,227,766.0168. It is also the floor of sqrt(10) × 10^8, because sqrt(10) ≈ 3.162277660168379 and multiplying by 10^8 gives about 316,227,766.0168. As such, 316,227,766 serves as a precise integer approximation to a scaled form of the square root of ten.

Applications and context: In computing and numerical methods that use fixed-point arithmetic, 316,227,766 can be used as an 8-decimal fixed-point representation of sqrt(10), representing the value sqrt(10) × 10^8 truncated to an integer. This enables fast integer-based approximations of operations involving sqrt(10) without floating-point arithmetic. It is an approximation rather than an exact value; the true sqrt(10) is irrational.

Related concepts: sqrt(10), fixed-point arithmetic, numerical approximation, integer representations of irrational constants.

See also: sqrt(10), fixed-point arithmetic, numerical approximation.