High School

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Using a while loop, determine how many terms are required so that the true error is less than \(10^{-2}\). Report this number of terms.

Options:
A) 10
B) 100
C) 1000
D) 10000

Answer :

Final answer:

To determine the number of terms required so that the true error is less than[tex](10^2),[/tex] you can use a while loop. The true error can be calculated by subtracting the actual value from the estimated value. The while loop will continue until the true error is less than [tex](10^2).[/tex]

Explanation:

To determine the number of terms required so that the true error is less than [tex](10^2),[/tex] you can use a while loop. The true error can be calculated by subtracting the actual value from the estimated value. The while loop will continue until the true error is less than[tex](10^2)[/tex]

Here is an example of how to use a while loop to determine the number of terms:

estimated_value = 0
counter = 0
while true_error >= 100:
counter += 1
estimated_value += term
true_error = abs(actual_value - estimated_value)
print(counter)

In this code, the variable 'estimated_value' is updated with each term added, and the counter keeps track of the number of terms. The true error is calculated as the absolute difference between the actual value and the estimated value. The while loop continues until the true error is less than 100.

Based on the given options, the correct number of terms required would be (b) 100.

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