Suppose we approximate the value of 1/128 by rounding to 3 decimal places. a) What would be the approximation? b) What is the number of significant digits in the approximation? c) What is the absolute error? d) What is the relative error?

Accepted Solution

Answer:a) The approximation is 0.008.b) One significant digitc) The absolute error is 0.0001875d) The relative error is of 2.4%.Step-by-step explanation:The formula for the absolute error is:Absolute error = |Actual Value - Measured Value|The formula for the relative error is:Relative error = |Absolute error/Actual value|The exact value of [tex]\frac{1}{128}[/tex] is 0.0078125Rounded to 3 decimal places it is 0.008(since the fourth digit is 8, bigger than 5, the third digit is rounded up).a) What would be the approximation?The approximation is 0.008.b) What is the number of significant digits in the approximation?The approximation has one significant digit, that is, the number of digits that were changed by the approximation.c) What is the absolute error?The measured value is 0.008The Actual value is 0.0078125SoAbsolute error = |Actual Value - Measured Value| = |0.0078125 - 0.008| = 0.0001875d) What is the relative error?The relative error is given by:[tex]R = \frac{0.0001875}{0.0078125} = 0.024[/tex]The relative error is of 2.4%.