A computer lacks a division instruction and performs division iteratively using the technique described on page 300. Suppose we wish to evaluate 327/940. How many cycles of iteration would it take to get an accuracy of ten decimal places?
What will be an ideal response?
Consider the following equation.
The value of 327/940 = 0.3478723404255319148936170212766 (first 10 decimal places in bold)
If we scale 327/940 we get 0.327/0.940 and Z = 1.000 – 0.940 = 0.060.
First iteration Q = 0.327 × 1.060 = 0.34662 (accurate to 2 dps)
Second iteration Q = 0.34662 × (1 + 0.0036) = 0.347867832 (accurate to 4 dps)
Third iteration Q = 0.347867832 × (1 + 0.00001296) = 0.34787234036710272 (accurate to 10dps assuming
rounding).
Therefore, only three iterations are necessary.
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