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View a Number as a Fraction
A rational number is a number which is either an integer or can be written in the form of a fraction, a
ratio of two integers. Usually, when a calculation is made, either by computer, calculator, or UltimaCalc,
the result is shown as a decimal number. For example the value of pi is shown
as 3.14159... etc.
If you calculate the value of pi, and then select the menu item View / As Ratios,
the multiple results window will open showing the value calculated and
then a list of ratios which have been calculated to various approximate numbers of digits. The first ratio
shown is 355/113, which is the value of pi to an accuracy of about 6 digits.
As
you look down the list, the fractions become more and more complicated in order to achieve the approximate
precision shown on the left. Such behaviour is only to be expected with the value of pi,
which is of course irrational, after all.
Another example: what is the value of 1/3+1/5-2/7? UltimaCalc will show the result
as 0.2476190... and shows this as the ratio 26/105. The result is the same
for all levels of accuracy, indicating that this ratio is the exact answer.
An alternative to using the menu item is to hold down the Control and Shift keys and press R. This will cause the current expression to be calculated first, and then shown as a ratio. When choosing to see the result as a rational number, remember that UltimaCalc uses the last value it calculated, and the menu item View / As Ratios does not calculate the current expression first. Therefore, if you change the expression in the entry box, remember to calculate it before choosing to look at it as a rational number if you use the menu item.
After viewing a value as a ratio, the display will revert to normal when you next evaluate an expression. If you set UltimaCalc to display in hexadecimal, ratios will also be shown in hexadecimal.