this post was submitted on 27 Jun 2024
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Science Memes

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[–] apolo399 2 points 5 months ago* (last edited 5 months ago) (1 children)

Sure, let's do it in base 3. 3 in base 3 is 10, and 3^(-1) is 10^(-1), so:

1/3 in base 10 = 1/10 in base 3
0.3... in base 10 = 0.1 in base 3

Multiply by 3 on both sides:

3 × 0.3... in base 10 = 10 × 0.1 in base 3
0.9... in base 10 = 1 in base 3.

But 1 in base 3 is also 1 in base 10, so:

0.9... in base 10 = 1 in base 10

[–] [email protected] -3 points 5 months ago (1 children)

You're having to use ... to make your conversion again. If you need to to an irrational number to make your equation correct, it isn't really correct.

[–] apolo399 4 points 5 months ago

Do you know what an irrational number is?