A student multiplied a number by
13
11
​
instead of
11
13
​
. What is the percentage error in the calculation?

Let the number be the product of the denominators, i.e., 13×11=143.
The correct result should be:

Correct Result=143×
11
13
​
=13×13=169
The incorrect result obtained by the student is:

Incorrect Result=143×
13
11
​
=11×11=121
Error in calculation:

Error=Correct Result−Incorrect Result=169−121=48
Percentage error is calculated with respect to the correct value:

Percentage Error=(
Correct Result
Error
​
)×100%
Percentage Error=(
169
48
​
)×100%≈28.402%
Therefore, the percentage error is 28.4%.