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Are my calculations below about 3-digit chopping, 3-digit rounding, and relative errors correct?

given 4/5 * 1/3:

Exact value: 0.2666666666666667
3-digit chopping: 0.266, its relative error: 0.0025
3-digit rounding: 0.266, its relative error: 0.0025

For another example, (1/3 - 3/11) + 3/20:
Exact value: 0.2106060606060606
3-digit chopping: 0.210, its relative error: 0.0029
3-digit rounding: 0.211, its relative error: 0.002

3rd example, (1/3 + 3/11) - 3/20:
Exact value: 0.4560606060606061
3-digit chopping: 0.456, its relative error: 0.000133
3-digit rounding: 0.456, its relative error: 0.00233

ice1000
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2D3D4D
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    In the second and third example the values are swapped. And in the third you cannot chop or round to $0.455$. – gammatester Feb 01 '16 at 09:13
  • @gammatester thanks, I have fixed the issue based on your comment. For the 3rd one, why can I not chop to 0.456? - okay, 0.455 you mean, I have changed it. please review now. – 2D3D4D Feb 01 '16 at 09:36
  • @gammatester is the relative errors correct? – 2D3D4D Feb 01 '16 at 09:38
  • I assume you always use absolute values, otherwise you have to be more specific. In the second example rounding gives an relative error $0.00187$. This may be rounded to $0.002$ but I strongly suggest that you use a single consistent format for your error values. In the third ex. you have only adjusted the value but not the error for rounding. – gammatester Feb 01 '16 at 09:48
  • In the first, your "exact value" is not correct. You cannot represent the exact value of $\frac 4{15}$ with any finite decimal. It is a rounded value, but with a larger number of decimals than $3$. The same applies to the other examples. When you say exact value you should mean it. Then the three digit rounding is wrong. It should be $0.267$ and the relative error is smaller than chopping to $0.266$ – Ross Millikan May 21 '22 at 03:47

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