A student multiplied a number by
13
6
instead of
6
13
. What is the percentage error in the calculation?
- A369.44 percent
- B$39.35 percent
- C184.72 percent
- D78.7 percent
Solution & Step-by-step Explanation
Let the number be the product of the denominators of the two fractions to avoid fractions in calculation.
Let the number = 6×13=78.
Correct value = 78×
6
13
=13×13=169
Incorrect value obtained = $78 \times \frac{6}{13} = 6 \times 6 = 36
Error in calculation = Correct Value−Incorrect Value
Error=169−36=133
Percentage error is calculated with respect to the correct value:
Percentage Error=(
Correct Value
Error
)×100%
Percentage Error=(
169
133
)×100%≈78.698%≈78.7%
Let the number = 6×13=78.
Correct value = 78×
6
13
=13×13=169
Incorrect value obtained = $78 \times \frac{6}{13} = 6 \times 6 = 36
Error in calculation = Correct Value−Incorrect Value
Error=169−36=133
Percentage error is calculated with respect to the correct value:
Percentage Error=(
Correct Value
Error
)×100%
Percentage Error=(
169
133
)×100%≈78.698%≈78.7%