A student multiplied a number by 2/5 instead of the intended 5/2. What is the percentage error in the result relative to the correct value?

Introduction / Context:
Miscalculations that invert a factor are common. The correct multiplier is 5/2, but the student used 2/5. We measure percentage error as the deviation from the correct result divided by the correct result, times 100%.

Given Data / Assumptions:
Correct factor = 5/2 = 2.5. Actual factor = 2/5 = 0.4.

Concept / Approach:
Let the true answer be T = 2.5N. The student’s answer A = 0.4N. Percentage error = |T − A| / T * 100%. Since factors scale the same base N, N cancels, leaving a comparison of the factors only.

Step-by-Step Solution:

Verification / Alternative check:
Using any N (say N = 10): Correct result = 25; student result = 4; error = 21; 21/25 * 100 = 84%.

Why Other Options Are Wrong:
82%, 86%, and 89% are plausible distractors from rough rounding. 80% corresponds to a different pair of factors, not this specific inversion.

Common Pitfalls:
Using the wrong base for percentage error (e.g., dividing by the wrong result). Always divide by the correct result when computing error percentage.

Final Answer:
84%