Absolute error; relative error and percentage error and Geometric meaning of differentials and algorithm

Explain percentage error

The decrease in percentage error

Explain relative error

The unit of percentage error is

The formula for percentage error is

The diameter of a wire as measured by a screw gauge was found to be 0.026 cm, 0.028 cm, 0.029 cm, 0.027cm, 0.024cm and 0.027 cm. Calculate (i) mean value of diameter (ii) mean absoulte error (iii) relative error (iv) percentage error. Also express the result in terms of absolute error and percentage error.

Following observations were taken with a vernier callipers while measuring the length of a cylinder : 3.29 cm,3.28 cm,3.31 cm,3.28 cm,3.27 cm,3.29 cm,3.20 cm . Then find : (a) Most accurate length of the cylinder (b) Absolute error in each observation (c) Mean absolute error (d) Relative error (e) Percentage error Express the result in terms absolute error and percentage error.

The diameter of a wire as measured by screw gauge was found to be 2.620, 2.625, 2.630, 2.628 and 2.626 cm. Calculate (a) mean value of diameter (b) absolute error in each measurement (c) mean absolute error (d) fractional error (e) percentage error (d) (f) Express the result in terms of percentage error

A physical quantity X is given by X=(a^(2)b^(2))/(sqrt(c).d) Find the relative error and percentage error in X if percentage errors in a,b,c and d are 1%,3%,4% and 2% respectively.

The percentage errors in the above problem is