Question

If the percent difference between two measured values, \[4.6{\text{ cm}}\] and \[5.0{\text{ cm}}\] is \[n\% \]. Find \[n\]? (Round off to the closest integer)

Answer 1

Hint: Here, we will the formula to calculate percent difference \[n\% = \dfrac{{{\text{Absolute difference}}}}{{{\text{Average}}}} \times 100\], where absolute difference is \[\left| {{E_2} - {E_1}} \right|\] and average is \[\dfrac{{\left| {{E_2} + {E_1}} \right|}}{2}\]. From the question let us take \[{E_1} = 4.6\] and \[{E_2} = 5.0\] and substitute in the formula to find the required value.

Complete step by step answer:

We are given that the two measured values, \[4.6{\text{ cm}}\] and \[5.0{\text{ cm}}\].
Let us assume that \[n\% \] is the percent difference between two measured values, \[4.6{\text{ cm}}\] and \[5.0{\text{ cm}}\].
So, we will instruct to compare the results of two measurements when there is no known or accepted value.
We know that the comparison is expressed as a percent difference, which is the ratio of the absolute difference between the experimental values \[{E_1}\] and \[{E_2}\] to the average or mean value of the two results expressed as a percent, \[n\% = \dfrac{{{\text{Absolute difference}}}}{{{\text{Average}}}} \times 100\], where absolute difference is \[\left| {{E_2} - {E_1}} \right|\] and average is \[\dfrac{{\left| {{E_2} + {E_1}} \right|}}{2}\].
So, we have
\[ \Rightarrow n\% = \dfrac{{\left| {{E_2} - {E_1}} \right|}}{{\dfrac{{\left| {{E_2} + {E_1}} \right|}}{2}}} \times 100\]
Consider \[{E_1}\] and \[{E_2}\] from given information, we get
\[{E_1} = 4.6\]
\[{E_2} = 5.0\]
Substituting the value of \[{E_1}\] and \[{E_2}\] in the above formula of percent difference, we get
\[
   \Rightarrow n\% = \dfrac{{\left| {5.0 - 4.6} \right|}}{{\dfrac{{\left| {5.0 + 4.6} \right|}}{2}}} \times 100 \\
   \Rightarrow n\% = \dfrac{{\left| {0.4} \right|}}{{\dfrac{{\left| {9.6} \right|}}{2}}} \times 100 \\
   \Rightarrow n\% = \dfrac{{0.4}}{{4.8}} \times 100 \\
   \Rightarrow n\% = 8\% \\
 \]
Hence, the required value is 8.

Note: We need to know that the absolute value of any positive number is the number itself and the absolute value of any negative number is the positive value of that number. We do not have to use any unit in the final answer. We know that a percent difference is a difference between two values divided by the average of the values shown as a percentage.