WHEN 0.997^6 WAS COMPUTED BY A STUDENT, HIS RESULT WAS 0.9817. FIND THE PERCENTAGE ERROR, CORRECT TO THREE DECIMAL PLACES
0.997^6 = 0.9821
error: 0.0004
% error: 0.0004/.9821 = 0.0004073 = 0.04%
AB stop talking in caps, it seems like you're yelling at people.
0.0004/0.9824
=0.004%
No, that's not correct.
0.997^6 is approximately equal to 0.9821 (rounded to four decimal places).
The absolute error is:
|0.9817 - 0.9821| = 0.0004
The relative error is:
0.0004 / 0.9821 = 0.00040728
We convert the relative error to a percentage by multiplying it by 100:
0.00040728 x 100% = 0.040728%
Rounded to three decimal places, the percentage error is approximately 0.041%.
To find the percentage error, we need to compare the student's result with the actual result and express the difference as a percentage of the actual result.
Step 1: Determine the actual result
To find the actual result, we need to reverse the calculation done by the student. We need to find the sixth root of 0.9817.
Actual Result = (0.9817)^(1/6) ≈ 0.9963 (rounded to four decimal places)
Step 2: Calculate the difference
The difference between the actual result and the student's result is:
Difference = Actual Result - Student's Result ≈ 0.9963 - 0.9817 ≈ 0.0146
Step 3: Calculate the percentage error
Percentage Error = (Difference / Actual Result) * 100
Percentage Error = (0.0146 / 0.9963) * 100 ≈ 1.467%
Therefore, the percentage error, correct to three decimal places, is approximately 1.467%.