1. define X as 0.999999 . . . .
2. multiply X by 10: ( 10X )
3. We know that 10 times 0.999999 = 9.999999 . . . So 10X = 9.999999. . .
4. Now subtract X from 10X : 9.999999 . . . -- 0.999999. . . . which = 9. (the parts to the right of the decimal point disappear because they are equal to each other)
5. So 9X = 9
6. and if 9X = 9, then X must = 1
7. Substituting for X from 1. above, 0.99999 . . . . = 1
2. multiply X by 10: ( 10X )
3. We know that 10 times 0.999999 = 9.999999 . . . So 10X = 9.999999. . .
4. Now subtract X from 10X : 9.999999 . . . -- 0.999999. . . . which = 9. (the parts to the right of the decimal point disappear because they are equal to each other)
5. So 9X = 9
6. and if 9X = 9, then X must = 1
7. Substituting for X from 1. above, 0.99999 . . . . = 1
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