@V8archie - If you can explain to me what recurring decimals do actually mean then I would be grateful. Iâ€™m here to learn, not antagonise.Or you could try to understand what recurring decimals actually mean and also the limitations of calculators.
It's rather easier than trying to guess which answers are rational and which aren't.
If I can find all these answers in a text book, please point me in the right direction and save your effort.
So, if a recurring decimal is not a real number, rather a representation, what real number does say 0.333 represent. It represents a 1/3
So, Iâ€™m assuming here that all fractions are real numbers and all recurring decimals represent an expressible fraction.
I also assume you can flit between representative numbers and real numbers in the same calculation. For example, if I divide 1 by 3 I come up with the representative decimal 0.333 but if I go on to multiply that by 6 I arrive back at the real number â€˜2â€™.
However, if I work fractionally the first calculation is 1/3 and my second is 2.
So for what use does the representative decimal serve if a fraction does the same job?
If decimal representation is by its very nature â€˜approximateâ€™ then how is this anomaly allowed to function when a real number fraction does the same job but is perfect (not approximate).