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Find the errors?

Find the absolute, relative and percentage errors when a) 2/3 is approximated to 0.667, b) 1/3 is approximated to 0.333, and c) true value is 0.50 and its calculated value was 0.49.
 
For part a), I got 0.00033 for the absolute error. Please use latex and show the work, thanks.
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2 Answers


a) Absolute error =| Approx. value - True value | = | 0.667 - 2/3 | = 1/3000

    Relative error = Absolute error/True value = (1/3000)/(2/3) = 0.0005 
   
    Percentage error = 0.05%

b) Absolute error = | Approx. value - True value | = | 0.333 - 1/3 | = 1/3000

    Relative error = Absolute error/True value = (1/3000)/(1/3) = 0.001

    Percentage error = 0.1%

c). We use absolute, relative and percentage errors when judge how close we came to duplicating the correct data in an experiment. It's all about calculating the experimental error.

- first: find the absolute value of a difference between the experimental value (what you got in the experiment) and the accepted/theoretical value (the true value). This value is your 'error'.

- second: divide this difference (between the experimental value and the accepted value) by the accepted value.

- third: convert the decimal number into a percentage by multiplying it by 100 to make the value a percent.

(| 0.49 - 0.50 | / 0.50) * 100 = 0.02 = 2%
           ↑                                         
absolute error = 0.01                         
                                                      
            relative error = 0.02              
                                                        
                               percentage error = 2% 

Comments

Percentage error is the relative error expressed as a percentage.
I set it up as a table in LaTex:
 
\begin{document}

\begin{tabular}{l|lll}
& Absolute & Relative & Percent \\ \hline
.667 for 2/3 & 1/3000 & 1/2000 & 0.05 \\
.333 for 1/3 & 1/3000 & 1/1000 & 0.1 \\
.49 for .50 & .01 & .02 & 2%
\end{tabular}

\end{document}
 
For a) and b), the absolute errors should be given as fractions (1/3000), not decimals.

Comments

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