Can someone please explain to me why fractions are a better alternative

Try to write 1/3 with decimals

>>8709799
>better
>not prettier

Because decimals are fractions with only powers of ten as the denominator.

>>8709794
Depends if you're actually doing math or just need a useful result. Fractions are pure answers and can be further transformed by calculation as needed. Converting to decimal only cuts off information. If you're doing some engineering all you need is enough places after the decimal and a small enough error at the end.

>>8709794
less expressive and harder to use

>>8710028
Exactly


>>8709794

Can you imagine saying it is 1.0166666666666666667 o'clock instead of 1:01?

fractions look cooler than decimals

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>>8709794
REAL NUMBERS CAN'T EXIST

Theyre easier to work with algebraically.

>>8709799
[math]
0.\overline{3}
[/math]

>>8709799
[math] 0.1_3 [/math]

Fractions generalise much more directly when you are considering the fields of fractions...

Because fractions maintain more information (all of it in fact) of a rational number during calculation.

>>8710277
>base 3
>decimal
Anon, I...

>>8710255
Now try to put that into a calculator or computer, ya dumb fuk.

>>8709794
Fractions are lossless codecs
Decimals are MP3 shit

>>8710372
https://www.wolframalpha.com/input/?i=3*.333...

>>8710491
exactly

were you trying to be smart and failed?

Any decent computer algebra system will even let you specify repeating decimals and then convert that back to fractions before doing calculations on it, but you didn't even bother doing that.

>>8710517
>and then convert that back to fractions

prove it

>>8709794
some decimals are irrational and its really annoying to deal with numbers that has no end

>>8709804
1/3 + 1/3 + 1/3 = 1
0,333 + 0,333 + 0,333 != 1

>>8710387
Spotted the CS brainlet who doesn't get maths.

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>>8710702
>0,333 + 0,333 + 0,333 != 1

0.333 + 0.333 + 0.333 = 0.999

Also, goddamn euros and their commas.

>>8710702
Firstly, [math]\frac 1 3 \neq 0.333; \; \frac 1 3 = 0.\bar 3 = 0.333...[/math]
Secondly, [math]0.333 + 0.333 + 0.333! \neq 1[/math]

>>8710887
[math] 0.333! + 0.333 + 0.333 ≈ 1.55901886795 [/math]

At best it's the same, at worst it's an approximation.