Convert decimal number to rational: Difference between revisions

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'''Solution'''

~~'''~~Case 1. Without repeating digits~~'''~~

=== Case 1. Without repeating digits===

The Fōrmulæ '''Rationalize''' expression converts from decimal numberts to rational in lower terms.

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[[File:Fōrmulæ - Convert decimal number to rational 02.png]]

[[File:Fōrmulæ - Convert decimal number to rational 03.png]]

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[[File:Fōrmulæ - Convert decimal number to rational 04.png]]

~~'''~~Case 2. With repeating digits~~'''~~

=== Case 2. With repeating digits ===

Fōrmulæ '''Rationalize''' expression can convert from decimal numbers with infinite number of repeating digits. The second arguments specifies the number of repeating digits.

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[[File:Fōrmulæ - Convert decimal number to rational 06.png]]

In the following example, a conversion of the resulting rational back to decimal is provided in order to prove that it was correct:

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[[File:Fōrmulæ - Convert decimal number to rational 10.png]]

[https://en.wikipedia.org/wiki/0.999... 0.999... is actually 1]:

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[[File:Fōrmulæ - Convert decimal number to rational 12.png]]

~~'''~~Programatically~~'''~~

=== Programatically ===

Even when rationalization expressions are intrinsic in Fōrmulæ, we can write explicit functions:

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[[File:Fōrmulæ - Convert decimal number to rational 15.png]]

[[File:Fōrmulæ - Convert decimal number to rational 16.png]]