A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation.

To calculate the percentage error when a student multiplied a number by 3/5 instead of 5/3, you can follow these steps:

1. Calculate the actual result when multiplying by 5/3.
2. Calculate the result obtained when multiplying by 3/5.
3. Find the absolute difference between the actual result and the obtained result.
4. Calculate the percentage error.

Let's do the calculations:

Actual result (multiplying by 5/3): Let the number be "x." Actual result = (5/3) * x

Obtained result (multiplying by 3/5): Obtained result = (3/5) * x

Absolute difference between actual and obtained results: Absolute difference = |(5/3) * x - (3/5) * x|

Calculate the percentage error: Percentage error = (Absolute difference / Actual result) * 100

Now, plug in the values:

Percentage error = [|(5/3) * x - (3/5) * x| / ((5/3) * x)] * 100

Percentage error = [|(5/3 - 3/5) * x| / ((5/3) * x)] * 100

Percentage error = [(16/15) * x / ((5/3) * x)] * 100

Percentage error = [(16/15) / (5/3)] * 100

Percentage error = [(16/15) * (3/5)] * 100

Percentage error = [(16/25)] * 100

Percentage error = 64%

So, the percentage error in the calculation is 64%.