Suppose is an approximation to a nonzero quantity x . This question pertains to IEEE floating point standard 754-1985. Double precision allocates more bits to the mantissa. Therefore numbers can be represented more accurately.
Double precision allocates more bits to the exponent.
Therefore much larger and smaller numbers can be represented. Give a simple example to illustrate the phenomenon. Think about the relative merits of the bisection and secant methods, then answer the following questions. The secant method normally converges much more rapidly. The bisection method always converges.