Answer:
a) e1 = 155.5%
b) e2 = 9.168%
e2 < e1
Explanation:
To solve the problem we need to calculate the absolute error between Ya and Ye where Ya is the approximate value (using 3-digit chopping) and Ye is the exact value. To calculate Ye we need to take all the decimals when solving the equation and to find Ya we need to take 2 decimals after performing any operation inside brackets to solve the equation, the percent relative error e is calculated using abs((Ya-Ye)/(Ye))*100%
a)
X=1.37 3-digit approximation Real value
(X*X)*X 2.571353 2.56
-7*(X*X) -13.1383 -13
8X 10.96 10.9
-0.35 -0.35 -0.35
Total 0.043053 0.11
Therefore the error e1 is abs((0.11-0.043053)/(0.043053))*100 = 155.5%
b)
X=1.37 3-digit approximation Real value
((X-7)*X+8)*X 0.393053 0.397
-0.35 -0.35 -0.35
Total 0.043053 0.047
Therefore the error e2 is abs((0.047-0.043053)/(0.043053))*100 = 9.168%
The error e2 is much smaller than e1 this is because the second equation was factorization in such a way that the number of operations was reduced therefore the cumulative error is reduced.
