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If percentage error in measurement of quantities A,B,C,D are 1%,2%,3%,4% respectively the percentage error in measurement of z=A^2B^1/3/C^1/3D^1/4?
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If percentage error in measurement of quantities A,B,C,D are 1%,2%,3%,...


Calculation of Percentage Error in z

  1. Given Data:

    Percentage error in A: 1%

    Percentage error in B: 2%

    Percentage error in C: 3%

    Percentage error in D: 4%


  2. Formula for z:

    z = A^2 * B^(1/3) / (C^(1/3) * D^(1/4))


  3. Calculating the Percentage Error:

    To calculate the percentage error in z, we need to find the individual contributions of errors in A, B, C, and D to the overall error in z.

    We can do this by taking the partial derivative of z with respect to each variable and then multiplying by the percentage error of that variable.

    After simplifying, we get the formula for percentage error in z as:

    Percentage Error in z = 2 * (Percentage Error in A) + (1/3) * (Percentage Error in B) - (1/3) * (Percentage Error in C) - (1/4) * (Percentage Error in D)


  4. Substitute Given Values:

    Substitute the given percentage errors into the formula:

    Percentage Error in z = 2 * 1% + (1/3) * 2% - (1/3) * 3% - (1/4) * 4%

    Percentage Error in z = 2% + 0.67% - 1% - 1%

    Percentage Error in z = 0.67%




Conclusion:
The percentage error in the measurement of z is approximately 0.67%.
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If percentage error in measurement of quantities A,B,C,D are 1%,2%,3%,4% respectively the percentage error in measurement of z=A^2B^1/3/C^1/3D^1/4?
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