piclist 2001\06\01\115058a >
Thread: Brain Burp Rounding??
face picon face BY : Dipperstein, Michael email (remove spam text)

> From: Alan B. Pearce [@spam@A.B.Pearce.....spamRL.AC.UK]
> >Given:
> >  x = 0.9(repeating)
> >Multiply both sides by 10:
> >  10x = 9.9(repeating)
> >Subtract x from both sides:
> The fallacy in this argument is that at the end x->1, as any repeating
> number is not exact.

I don't understand where the fallacy lies.  A repeating number *is* exact as
long as it isn't truncated.

1/3 is exactly .3 (repeating)

1/3 is not exactly .3333333 or .3333333333 or any truncated version.

Along that line here's another simple Junior High School algebra proof that 1 =
.9 repeating.

1/3 = .3 repeating

multiply both sides by 3

(1/3)*3 = 3 * (.3 repeating)

1 = .9 repeating


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