1.1.2 Exact and Approximate ResultsA standard electronic calculator does all your calculations to a particular accuracy, say ten decimal digits. With Mathematica, however, you can often get exact results. Mathematica gives an exact result for  , even though it has 31 decimal digits. | |
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You can tell Mathematica to give you an approximate numerical result, just as a calculator would, by ending your input with //N. The N stands for "numerical". It must be a capital letter. Section 2.1.3 will explain what the // means. | This gives an approximate numerical result. | |
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| Mathematica can give results in terms of rational numbers. | |
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| //N always gives the approximate numerical result. | |
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| expr //N | give an approximate numerical value for expr |
Getting numerical approximations. When you type in an integer like 7, Mathematica assumes that it is exact. If you type in a number like 4.5, with an explicit decimal point, Mathematica assumes that it is accurate only to a fixed number of decimal places. | This is taken to be an exact rational number, and reduced to its lowest terms. | |
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| Whenever you give a number with an explicit decimal point, Mathematica produces an approximate numerical result. | |
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| Here again, the presence of the decimal point makes Mathematica give you an approximate numerical result. | |
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| When any number in an arithmetic expression is given with an explicit decimal point, you get an approximate numerical result for the whole expression. | |
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