this post was submitted on 03 Jun 2025
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[–] Knock_Knock_Lemmy_In@lemmy.world 2 points 2 days ago (12 children)

For example, they allow you to write

1/3 + 1/3 + 1/3 = 1

Which is not possible in decimal

[–] axEl7fB5@lemmy.cafe 1 points 1 day ago (5 children)

Tf you mean?? You can write it in a repeating decimal as 0.333.... using ellipsis. https://wiki.froth.zone/wiki/Repeating_decimal

[–] Knock_Knock_Lemmy_In@lemmy.world 0 points 1 day ago* (last edited 1 day ago) (4 children)

So you think

0.333.... + 0.333.... + 0.333.... = 1

Is clearer and more concise than

1/3 + 1/3 + 1/3 = 1

Fractional representation is the method for rational numbers, particularly if they are part of an intermediate calculation.

Decimals are lossy, fractions aren't.

[–] axEl7fB5@lemmy.cafe 1 points 22 hours ago* (last edited 22 hours ago) (1 children)

No because you said this:

If you want to precisely write to infinity you write 1/3.

You can also precisely write to infinity if you write 0.333....

Decimals are lossy, fractions aren’t.

Decimals aren't lossy, any fraction can be converted to decimal but it just takes longer to write.

[–] Knock_Knock_Lemmy_In@lemmy.world 1 points 21 hours ago (1 children)

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.

[–] axEl7fB5@lemmy.cafe 1 points 19 hours ago (1 children)

As soon as you use decimals in computer and human calculations, they become lossy.

What does lossy mean? I'm not trying to die on any hill, but I'm quite confused aswell.

[–] Knock_Knock_Lemmy_In@lemmy.world 1 points 12 hours ago

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.

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