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                      • Numbers representation, tolerance and precision

                      Comparison by rounding

                      Reading time: 1min

                      As you may have noticed, both significant figures and decimal places comparison methods use the truncation function. Conversely, you may be interested in replicating the same behaviour with the rounding function. Below you can find two alternative procedures to do so.

                      Using absolute error tolerance and a concrete number of decimals assertion

                      The first option will require combining two assertions we have previously analyzed: absolute error and a concrete number of decimals. If we want to check that the student's answer exactly has n decimal places, and these are identical to the correct answer first n decimal places after rounding, we need to set the error margin to 0.5·10-n and define the precision to n decimal places.  
                       
                      For instance, if the correct answer is   
                      19.586

                      Student Answer
                      Decimal places 19.6 19.59 19.58 19.587 19.586
                      1
                      2
                      3
                      4

                      Using a grading function

                      The second option will require some programming in CalcMe through a grading function. If we want to check that the first n decimal places of the student and correct answers are identical after rounding, we need to define the following user-defined routine (for n=2).  

                      Tip

                      You can see more about grading functions here.

                      For instance, if the correct answer is 19.586

                      Student Answer
                      Decimal places 19.6 19.59 19.58 19.587 19.586
                      1
                      2
                      3
                      4

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                      • Debugging (what to do if it isn't working)
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                      Comparison by rounding

                      Using absolute error tolerance and a concrete number of decimals assertion Using a grading function Tip

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