On 16 January 2013 08:57, Roger Hui <[email protected]> wrote: > ... > Let x=0.6242424 ... . Multiply x by 100 and subtract x, > > 100 x 62.4242424 ... > x 0.6242424 ... > ----- -------------- > 99 x 61.8 > > So 99 x = 61.8. Divide both sides by 99 and you get x=61.8%99 . Simplify > and you get x=103r165.
I would prefer the following derivation: Let x = 0.6(24). Multiply by 10 to isolate the repetend from the preceding part: 10x = 6+0.(24). Let y = 0.(24) (thus x = (6+y)/10), then 100y-y = 24, i.e. y = 8/33. Therefore x = (6+8/33)/10 = 103/165. This derivation is cleaner by treating explicitly the repetend, referring to a 'canonical' repeated fraction, and by making more easily obvious what the method is and why it works. Processing other fractions with the same repetend will share the derivation of y. Consider: Let x = 0.635(24), then 1000x = 635+0.(24). Let y = ... exactly the same as above ... Therefore x = (635+y)/1000 = (635+8/33)/1000 = 20963/33000. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
