A student multiplied a number by \(\frac{7}{4}\) instead of \(\frac{3}{5}\). Find the percentage error in the calculation.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(191\frac{2}{3}\%\)
The percentage error is the error as a percentage of the correct value. Taking the number as 20 (a number that 4 and 5 divide) keeps the values whole.
Correct value \(\displaystyle =\frac{3}{5}\times20=12\); value found \(\displaystyle =\frac{7}{4}\times20=35\)
Error \(=35-12=23\)
Percentage error \(\displaystyle =\frac{23}{12}\times100=\frac{575}{3}=191\frac{2}{3}\%\)
The percentage error is \(191\frac{2}{3}\%\).