Compute (22/70) ( / 10) using five-digit rounding arithmetic as follows. (Note i

Question

Compute (22/70) (/10) using five-digit rounding arithmetic as follows. (Note if your answer is between -1 and 1, then you must type 0.xxx for your answer. Do not use the floating point form.)

a. In five-digit rounding arithmetic, 22/70=  
b. In five-digit rounding arithmetic, /10=  
c. Then, in five-digit rounding arithmetic, 22/70/10 =  
Now, compute 22/70/10 using the full accuracy of your calculator/computer and enter the result to the ninth decimal
d. To the ninth decimal, 22/70/10 =  
use that as the exact result to compute (enter your final result to at least the third decimal place)
e. Relative Error =

Explanation / Answer

a. In five-digit rounding arithmetic, 22/70= 0.31428571 ~~ 0.31429
b. In five-digit rounding arithmetic, /10= 0.314159 ~~ 0.31416
c. Then, in five-digit rounding arithmetic, 22/70/10 = 0.00012644 ~~ 0.00013
Now, compute 22/70/10 using the full accuracy of your calculator/computer and enter the result to the ninth decimal
d. To the ninth decimal, 22/70/10 = 0.000126448
use that as the exact result to compute (enter your final result to at least the third decimal place)
e. Relative Error = (0.00013 - 0.000126448)
------------------------------------ = 0.0273230 ~~ 0.027
0.00013

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