Convert decimal number to rational: Difference between revisions

'''Solution'''

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

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

[[File:Fōrmulæ - Convert decimal number to rational 01.png]]

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

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

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

'''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.

[[File:Fōrmulæ - Convert decimal number to rational 05.png]]

[[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:

[[File:Fōrmulæ - Convert decimal number to rational 07.png]]

[[File:Fōrmulæ - Convert decimal number to rational 08.png]]

[[File:Fōrmulæ - Convert decimal number to rational 09.png]]

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

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

[[File:Fōrmulæ - Convert decimal number to rational 11.png]]

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

'''Programatically'''

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

[[File:Fōrmulæ - Convert decimal number to rational 13.png]]

[[File:Fōrmulæ - Convert decimal number to rational 14.png]]

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

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

[[File:Fōrmulæ - Convert decimal number to rational 17.png]]

[[File:Fōrmulæ - Convert decimal number to rational 18.png]]

[[File:Fōrmulæ - Convert decimal number to rational 19.png]]

[[File:Fōrmulæ - Convert decimal number to rational 20.png]]