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Perform the following computations (i) exactly, (ii) using three-digit chopping arithmetic, and (iii) using three-digit rounding...

Perform the following computations (i) exactly, (ii) using three-digit chopping arithmetic, and (iii) using three-digit rounding arithmetic. Then compute the relative errors of the final results.

(a) 3/ 4 + 1 /5

(b) ( 3 /4 )( 1 /5 )

(c) ( 1 /3 − 3 /11 ) 4 5 + 3 20

(d) ( 1/ 3 + 3 /11 ) + 3/ 20

(e) Repeat (a) and (c), above, now using four digits. Does this give greater accuracy? Is a k + 1 digit computer always more accurate than a k digit one?

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