You can contemplate Whole Number, Single-Digit solutions (a,b,c,d) to this:
You suggested one such solution:
a = 2
b = d = 7
c = 3
Hello, thamathkid1729!
What is the relationship between these two decimals?
How would I find other pairs of decimals with the same relationship?
We have: .
. . . . . . . .
We have: .
Therefore:
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
This can be readily generalized.
For four-digit decimal cycles: .
Therefore:
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
For your amusement, a seven-digit cycle:
. .