Question

Pankaj expected to earn $\$425$ in a week. In fact, he earned $\$500$ . Calculate the percentage error.
A. $25\%$
B. $15\%$
C. $11.5\%$
D. None of these

Answer 1

Hint: First analyze the question and then find out the estimated value and true value and then take the difference of one value from another. After that divide it with the true value and multiply it with $100$as in the given formula: $\%\text{ Error}=\left| \dfrac{T-E}{T} \right|\times 100$ . Then finally add a percentage symbol to represent percent error value.

Complete step-by-step answer:
Let’s first understand what is percentage error, so basically it indicates how big our errors are when we measure something in an analysis process of an experiment. Smaller percent errors indicate that we are close to the accepted or original value. For example, a $1\%$ error indicates that we got very close to the accepted value, while $40\%$ means that we were quite a long way off from the true value.
Technically, Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.
Now, the percent error formula is:
$\%\text{ Error}=\left| \dfrac{T-E}{T} \right|\times 100$
Where,
$T=$ True or actual value
$E=$ Estimated value
Now to find the percent error in the question, we will have to substitute estimated value as $\$425$ and the true value as $\$500$ as given in the question.
Now, we have
$\%\text{ Error}=\left| \dfrac{T-E}{T} \right|\times 100=\left| \dfrac{500-425}{500} \right|\times 100=\dfrac{75}{500}\times 100=15\%$
Therefore, the correct option is B.

Note:Even if you ignore the sign in the formula of percent error formula, the order does not matter. But we need to subtract the original value from the determined value if we are keeping the negative signs. Measurement errors are often unavoidable due to certain reasons like hands can shake, material can be imprecise, or our instruments just might not have the capability to estimate exactly.