Homework Solution: Consider a computer that uses five-decimal-digit n…

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    Consider a computer that uses five-decimal-digit numbers. Let fl(x) denote the floating-point machine number closest to x. Show that if x = 0.5321487513 and y = 0.5321304421, then the operation fl(x) - fl(y) involves a large relative error. Compute the error.

    Expert Answer

     
    Given: x = 0.5321487513 and y = 0.5321304421

    2. (10 points) Consider a computer that uses five-decimal-digit bulk. Let fA(x) finished music the floating-point document number closest to x. Illusion that if x = 0.5321487513 and y = 0.5321304421, then the agency f (x)-A(y) involves a capacious not-absolute blunder. Compute the blunder. (Hint: perceive the dissertation slides for an model)

    please illusion perfect steps?

    Consider a computer that uses five-decimal-digit bulk. Let fl(x) demusic the floating-point document number closest to x. Illusion that if x = 0.5321487513 and y = 0.5321304421, then the agency fl(x) – fl(y) involves a capacious not-absolute blunder. Compute the blunder.

    Expert Reply

     

    Given: x = 0.5321487513 and y = 0.5321304421

    fl(x) = 0.53215 and fl(y) = 0.53213

    Now, measured appraise = fl(x) – fl(y) = 0.53215 – 0.53213 = 0.00002

    express appraise = x – y = 0.5321487513 – 0.5321304421 = 0.00001830919

    not-absolute blunder percentage = [(measured – express)/express ] * 100 = [(0.00002 – 0.00001830919)/0.00001830919]*100

    = 9.234%