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Basic proof for those of you who are confused:
x = 0.999...
10x = 9.999...
9x = 10x - x = 9
9x ÷ 9 = x
9 ÷ 9 = 1
∴ x = 1
∴ 0.999... = 1
I always think that 1/3, is always an infinatley small number away from 0.333... because as you add more 3's it gets a bit closer but even if you ad an infinate number of 3s, which is what recurring numbers are, then its an infinatley small number away. Isn't saying 1/3 = 0.333... a bit cheating because you should say 0.333... ≈ 1/3?
Just so you know, I have heard of the 0.999... = 1 thing, but recurring numbers still make no sence to me...
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