A student found the approximate value of 0.02548 correct to two places of decimal instead of two significant figures. Find the percentage error?
To find the percentage error, we need to calculate the absolute difference between the approximate value and the actual value, and then express it as a percentage of the actual value.
Given:
Approximate value = 0.02548 (rounded to two decimal places)
Actual value = unknown
Since the approximate value is rounded to two decimal places, we assume the actual value lies between 0.025475 and 0.025485 (by considering the next digit).
Let's assume that the actual value is x.
Absolute difference = |0.02548 - x|
To calculate the percentage error, we use the following formula:
Percentage error = (absolute difference / actual value) * 100
Since the actual value is unknown, we cannot calculate the exact percentage error without more information.
To determine the percentage error, we need to find the absolute difference between the approximate value and the actual value, and then express it as a percentage of the actual value.
To find the actual value, we need to consider two significant figures instead of two decimal places since the student mistakenly used decimal places.
To convert the approximate value to two significant figures:
0.02548 ≈ 0.025
Now, we can find the absolute difference:
Absolute difference = Actual value - Approximate value = 0.025 - 0.02548 = -0.00048
Next, we express the absolute difference as a percentage of the actual value:
Percentage error = (|Absolute difference| / Actual value) * 100
Since the absolute difference in this case is negative, we consider the magnitude:
Percentage error = (|-0.00048| / 0.025) * 100
Calculating this equation, we get:
Percentage error = (0.00048 / 0.025) * 100
Percentage error ≈ 1.92%
Therefore, the percentage error in this case is approximately 1.92%.