Find the absolute error for the answer of the following equation:
square root of 3.24 plus-minus 0.08 end root equal 1.80 plus-minus ?
To find the absolute error for the given equation, we need to calculate the difference between the actual answer and the given answer.
The equation is:
√3.24 ± 0.08 = 1.80 ± ?
To find the possible values for the square root of 3.24, we take the square root of the central value and subtract and add the uncertainty:
Lower value = √(3.24 - 0.08) = √3.16 ≈ 1.778
Upper value = √(3.24 + 0.08) = √3.32 ≈ 1.821
So the possible values for the square root of 3.24 are between approximately 1.778 and 1.821.
To find the absolute error, we need to find the difference between the given answer (1.80) and the upper and lower values:
For the upper value: Absolute error = |1.821 - 1.80| = 0.021
For the lower value: Absolute error = |1.778 - 1.80| = 0.022
Since the larger absolute error is 0.022, the absolute error for the given equation is approximately 0.022.