Numerical approximation involves finding a number X' that approximates the value of another number X. While numerical solutions are not exact, the goal is to obtain a solution close to the real solution. Significant figures are important in numerical methods because they designate the reliable digits in a number. Numerical errors originate from approximating exact mathematical quantities and can be truncation errors from approximations or round-off errors from limited significant figures. Relative error provides a way to account for magnitude and the true percent relative error measures accuracy. The Taylor series can be used to approximate functions as polynomials using values and derivatives at other points.