The fraction 1/3 is a compact and unambiguous representation—it doesn’t rely on an ellipsis or an understanding of infinite series to be interpreted. It can easily be used in later calculations (you never see … notation in algebra). It is a useful notation.
As soon as you use decimals in computer and human calculations, they become lossy.
I’m not really sure what hill you are trying to die on. Fractions are useful, even if you don’t know how to use them.
By lossy I mean rounding errors. Try to combine 2 or more recurring decimals in any function and you start loosing accuracy.
Mathematicians rarely use decimals (also they rarely use numbers). Everything stays in fractions. Maybe the very last step is delivered as a decimal, but rarely.
No because you said this:
You can also precisely write to infinity if you write 0.333…
Decimals aren’t lossy, any fraction can be converted to decimal but it just takes longer to write.
The fraction 1/3 is a compact and unambiguous representation—it doesn’t rely on an ellipsis or an understanding of infinite series to be interpreted. It can easily be used in later calculations (you never see … notation in algebra). It is a useful notation.
As soon as you use decimals in computer and human calculations, they become lossy.
I’m not really sure what hill you are trying to die on. Fractions are useful, even if you don’t know how to use them.
What does lossy mean? I’m not trying to die on any hill, but I’m quite confused aswell.
By lossy I mean rounding errors. Try to combine 2 or more recurring decimals in any function and you start loosing accuracy.
Mathematicians rarely use decimals (also they rarely use numbers). Everything stays in fractions. Maybe the very last step is delivered as a decimal, but rarely.