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It's ok to use decimals in fractions

Submitted by onevest in just_post

Each year is, on average, 365.25 days (with two places of precision).

So, if uniformly distributed, today is the birthday of 1/365.25 of the population!

I wouldn't say 4/1461, because 1. We lose the fact that we're dealing with an imprecise number, and 2. It's harder to see that and tie it to the fact that a year is about 365.25 days long.

I will travel back in time and fight my elementary school math teachers now.

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5

flabberghaster wrote

Yes, a fraction is a rational number. The rational numbers are the set Q such that for all x in Q, x = a/b for some integer a and b (b != 0).

Decimal notation is just a different way to write a rational number.

Since Q is closed under division meaning that a rational divided by a rational is guaranteed to return a rational number (except for division by zero), then having a fraction with a decimal in it is valid.

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bunnies wrote

Yes, a fraction is a rational number.

Is this actually true? 1/(2*pi) seems like a perfectly reasonable fraction to me. My intuitive feeling is that a fraction is just one quantity divided by another quantity, no matter the set membership.

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flabberghaster wrote

Oh i thought i remembered them as being rational, and that irrational ones were invalid. But i was wrong.

Flabbergaster demolished by logic and reason