﻿ Cosmos Apps - Approximate fraction of a decimal value

 Approximate fraction of a decimal value: Sometimes, mathematicians are interested in the reduction of a decimal number - with several decimal places - to a simple fraction - approximately. It's the purpose of this application. Using this calculation for the known value of PI, we can compute approximate fractions of its value reaching, for instance, the fraction  355 ÷ 113 ( = 3.1415929203539823 ...) - with an error of less than 2,668 * 10e-7. If we used this aproximate value for the calculation of the perimeter of a circumference with a million kilometers radius (1 000 000 000 meters), the error would be less than 534 meters. For the value of e, the natural logarithm, you will find a simple fraction - 2721 ÷ 1001 - with an error less than 1.1018 * 10e-7.

Value:

The program will also output the CF, continued fraction of the value. To convert, here's an example:

2.7647058823529411: CF = [2,1,3,4]  =
2 +
1
1 +
1
3 +
 1 4
=  2 + 13/17  =  47/17

http://cosmos.pt
2003- - Cosmos - Todos os direitos reservados