Q) A student was supposed to multiply a positive real number π with another positive real number π. Instead, the student divided π by π. If the percentage error in the studentβs answer is 80%, the value of π is.
π Additional InformationThe correct answer is \(\sqrt{5}\).
Explanation: Let the correct result be \( p \times q \). Instead, the student calculated \( \frac{p}{q} \). Let the percentage error be \( 80\% \). The percentage error can be expressed as: \[ \text{Percentage Error} = \frac{\left( \frac{p}{q} - p \times q \right)}{p \times q} \times 100 \] This simplifies to: \[ 80 = \frac{\left( \frac{p}{q} - p \times q \right)}{p \times q} \times 100 \] Letβs set up the ratio \( \frac{\frac{p}{q}}{p \times q} \), solve it, and use algebra to find that \( q = \sqrt{5} \).
Explanation: Let the correct result be \( p \times q \). Instead, the student calculated \( \frac{p}{q} \). Let the percentage error be \( 80\% \). The percentage error can be expressed as: \[ \text{Percentage Error} = \frac{\left( \frac{p}{q} - p \times q \right)}{p \times q} \times 100 \] This simplifies to: \[ 80 = \frac{\left( \frac{p}{q} - p \times q \right)}{p \times q} \times 100 \] Letβs set up the ratio \( \frac{\frac{p}{q}}{p \times q} \), solve it, and use algebra to find that \( q = \sqrt{5} \).
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