Question

A student multiplied a number by 5/11 instead 11/5 what is the percentage error

Answer 1

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Answer 2

Given:

student multiplied a number by 5/11 instead 11/5 what is the percentage error

Solution:

Assume that the number is $x$,

Multiply the number with $\[\frac{{11}}{5}\]$,

$\[ = \frac{{11x}}{5}\]$

Multiply the number with $\[\frac{{5}}{11}\]$,

$\[ = \frac{{5x}}{{11}}\]$

Find the % error in the calculation,

$\[ = \frac{{\frac{{11x}}{5} - \frac{{5x}}{{11}}}}{{\frac{{11x}}{5}}} \times 100\]$

$\[ = \frac{{121x - 25x}}{{11 \times 5}} \times \frac{5}{{11x}} \times 100\]$

$\[ = \frac{{96x}}{{121}} \times 100\]$

Solve further,

$\[ = \frac{{9600}}{{121}}\]$

$\[ = 79.3\% \]$

Hence, the parentage error in the calculation is 79.3%