4 ms·

Another intuition: All the decimals that recur are fractions with a denominator of 9. E.g. 0.1111.... is 1/9 0.7777.... is 7/9 It therefore stands to reason

by nly 3y ago

Another intuition: All the decimals that recur are fractions with a denominator of 9. E.g. 0.1111.... is 1/9 0.7777.... is 7/9 It therefore stands to reason that 0.99999.... is 9/9, which is 1

hoosieree 3y ago
That's a good one! Might replace my current favorite which is: Let x = 0.99... Then 10*x = 9.99... And if we subtract x from both sides, we get: 10x - x = 9.99... - x And since we already defined x=0.99... when we subtract it from 9.99..., we get 9x = 9 So we can finally divide both sides by 9: x = 1