10/3 gives an infinite answer, but if you can do this maybe you will get an answer?

Question

10/3 gives an infinite answer, but if you can do this maybe you will get an answer?

Get a 10cm string and divide to 3 sections zig zag for a shape like "N" so when all ends are together it is divided into 3 properly. It has to be broken somewhere (An atom)?

Ah we don't have good scale instruments to measure it, but mathematically we cannot divide 10 by 3 but imagine, if we had a super 100% perfect atomic scale equipments then we can divide. but my problem is it has to be broken somewhere right? Maybe half of the 1/3 of the atom or something again 1/3 and 1/3. Or 10/3 never can be solved even if we had super atomic scale instruments

I was considering only base 10 :D (I know when use other bases it seems to be fine)

Answer 1

Breaking a piece into identical smaller pieces is only limited by the tolerance of the measuring instruments you choose. And every measuring unit has a degree of error associated with it; so if you go to enough significant figures, likely the lengths will never be identical. i.e. 3.3333334 vs 3.3333332 vs 3.3333324 or something might all look identical to you.

Answer 2

Rather than using atomic-scale instruments, just calculate in base 3: instead of 10/3 = 3.3333... we get
101 / 10 = 10.1
which says exactly the same thing but takes only a few digits to write.

But as SteveK said, just because 10/3 doesn't have a finite base-10 decimal representation doesn't mean the number itself is inexact. It just means that if you insist in writing it in base-10 decimal notation you won't write the exact value of it. There are many ways of writing it exactly, of which 10/3 is the simplest.

Answer 3

If you had a string of atoms, you could divide it into three exactly equal parts only if the number of atoms you started out with was a multiple of three.

Answer 4

Read the answers to this same question a couple of days ago: http://au.answers.yahoo.com/question/index;_ylt=AgEAQCW2nzJwWW4BrSWuFWLh5gt.?qid=20070506042314AA1HHb1&show=7#profile-info-YxzODWakaa

10 divided by 3 gives an exact answer!