i got a little lost in all the fractions. i think i might have an idea of how to find them and how it all works, but i need to see more examples of this/work with the concept myself. also i was a little confused with the theorem in the section; i don’t think i see how that theorem is helpful. maybe when i have to use it i will see that it really is helpful.
i think it’s so interesting that we can use continued fractions to better approximate real numbers (with lots and lots of decimals). it makes a ton of sense when you think about it, but i never had. i always knew that if i wanted to accurately represent a number with crazy decimals, it was better to stick with the fraction. however, i never really thought about using a different fraction that would be a better, more exact representation/approximation of all those decimals. it makes so much sense.
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