Numeric computations

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Numeric computations use rational or irrational numbers written out in a specific base (usually binary for computers and calculators internally, decimal for input and output). In the case of irrational numbers, this means that the representation must be truncated at some point (hopefully far enough that the result will be good enough for practical purposes), and even rational numbers like $\scriptstyle {\frac {4}{3}}\,$ can suffer from loss of machine precision.

Most scientific calculators can accept input using a limited repertoire of symbols (e.g., $\scriptstyle {\sqrt {\pi }},\,\log ,\,\,$ ANS) but return numeric results only. Thus, we could input $\scriptstyle \pi +\pi \,$ and then press the equals key 47 times. The calculator would not recognize 150.79644737232 as approximately $\scriptstyle 48\pi \,$, and in fact ANS/48 might yield a result different enough from the calculator's representation of $\scriptstyle \pi \,$, e.g., 3.14159265359 (this differs from 3.14159265358979 by 0.00000000000020694557179).

Here is an example to try out on a scientific calculator with a 2-line display: (7 + 5√2)(7 - 5√2). Instead of –1, the calculator might answer –0.999999999.

See also

• Symbolic computations