Question

Charlie guesses that his dog weighs 34. 5 pounds. The dog actually weighs 32. 7 pounds. What is the percent error in Charlie’s guess, to the nearest tenth of a percent? 0. 05% 0. 5% 5. 2% 5. 5%.

Answer 1

Percent error is the amount of error to actual value, in percent. The percent error in Charlie’s guess is approximately: Option D: 5.5%

How to calculate the percent error?

Suppose the actual value and the estimated values after the measurement are obtained. Then we have:

Error = Actual value - Estimated value

To calculate percent error, we will measure how much percent of actual value, the error is, in the estimated value.

$\rm Percent \: Error = |\dfrac{Error}{Actual value}|\times 100 \\\\Percent \: Error = | \dfrac{\text{(Actual Value - Estimated Value)}}{Actual value}|\times 100$

(here |x| is such that it makes x non negative, thus, |-5| = 5, and |5| = 5)

For the given case, it is specified that:

Actual weight of dog = 32.7 pounds

Guessed weight of dog, by Charlie : 34.5 pounds.

Error = 32.7 - 34.5 = -1.8 pounds

Thus, percent error in Charlie's guess is calculated as:

$\text{Percent Error} = |\dfrac{-1.8}{32.7}| \times 100 \approx 5.5\%$

Hence, the percent error in Charlie’s guess is obtained approximately is given by: Option D: 5.5%

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