Answer:
a. 1.0833
Absolute Error = 0.416667
Relative Error = 1.250002
b. 0.0011070
Absolute Error = 0.0011070
Relative Error = 0.003321
Step-by-step explanation:
Given
1/3 = 0.333333
3/4 = 0.75
100/301 = 0.332226
a.
1/3 + 3/4
= 0.333333 + 0.75
= 1.083333
= 1.0833 ------ Approximated to 5 significant digits
Absolute Error = |Real Value - Estimated Value|
Relative Error = Absolute Error/Real Value
Assume 1/3 to be the real value and 3/4 to be the estimated value
Absolute Error = |0.333333 - 0.75|
Absolute Error = |-0.416667|
Absolute Error = 0.416667
Relative Error = 0.416667/0.333333
Relative Error = 1.250002
b.
1/3 - 100/301
= 0.333333 - 0.332226
= 0.001107
= 0.0011070 ----- Approximated to 5 significant digits
Assume 1/3 to be real value and 100/301 to be estimated value
Absolute Error = 0.333333 - 0.332226
Absolute Error = 0.0011070
Relative Error = 0.0011070/0.333333
Relative Error = 0.003321
Absolute and relative errors are approximation errors and they are due to the discrepancy between an exact value and some approximation to them.
The absolute error is the magnitude of the difference between the exact value and the approximation. The relative error is the absolute error divided by the magnitude of the exact value
