Calculation:

Let the number be x.

According to the question, the student multiplied x by 4/5 instead of 5/4.

So, the actual value of x should be (5/4)x, but the student got (4/5)x.

Percentage error = (Actual value - Approximate value) / Actual value x 100

= [(5/4)x - (4/5)x] / (5/4)x x 100

= (1/20)x / (5/4)x x 100

= 1/4 x 100

= 25%

Therefore, the percentage error in the calculation is 25%.

Explanation:

The question is about finding the percentage error in a calculation where a student multiplied a number by 4/5 instead of 5/4. This means that the student got an approximate value of the number, which is different from the actual value. The percentage error is a measure of how different the approximate value is from the actual value, expressed as a percentage of the actual value.

To solve the problem, we need to first find the actual value of the number. We know that the student should have multiplied the number by 5/4, so the actual value of the number should be (5/4)x. We also know that the student got an approximate value of the number, which is (4/5)x.

Next, we can use the formula for percentage error to find the percentage by which the approximate value differs from the actual value. The formula is (Actual value - Approximate value) / Actual value x 100. Substituting the values we have, we get:

Percentage error = [(5/4)x - (4/5)x] / (5/4)x x 100

Simplifying this expression, we get:

Percentage error = (1/20)x / (5/4)x x 100

Percentage error = 1/4 x 100

Percentage error = 25%

Therefore, the percentage error in the calculation is 25%. This means that the approximate value obtained by the student is 25% less than the actual value.