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:
- Calculate the actual result when multiplying by 5/3.
- Calculate the result obtained when multiplying by 3/5.
- Find the absolute difference between the actual result and the obtained result.
- 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%.
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