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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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.

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