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Old 2021-09-06, 10:16   #1
neskis
 
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Feb 2019

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Default Auxiliary fractions observation

I was watching a vedic math YouTube video on the concept of auxiliary fractions and noticed something about the prepended remainders. I am not well educated in mathematics and lack the proper terminology, so I have attached a photo. I'll do my best to explain an example and welcome any insight. Most likely a well known concept, but I'd like to learn more!

Ex: 1/39 = Auxiliary fraction first order 0.1/4
0.102225160401
The prepended remainders 0012214= 10510
AND
((40^6)-1)/399 = 105,025,641
*notice the 105 prepended to the repetend of 1/39.
(Also noted that 409510 = 3333334

I've worked out dozens of examples in many other bases and the same is always true. Another example is included in my photo.
Attached Files
File Type: pdf Mon, Sep 6, 2021, 10:07 AM.pdf (506.6 KB, 29 views)
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Old 2021-09-09, 16:18   #2
Dr Sardonicus
 
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Looks remarkably similar to the discussion in this thread.
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