This document discusses approximation and round-off error in engineering. It defines approximation as using an inexact value when the exact value is unknown or difficult to obtain. Approximations introduce errors from measurements in the real world. There are two main types of errors - truncation error from dropping digits during approximations, and rounding error from representing numbers with a fixed number of significant figures. The absolute error is the difference between the true and approximate values, while relative error is the percentage difference between the absolute error and true value. Understanding error is important for engineering applications that use numerical methods and measurements.