Mathematical Confusion!
0.999....
= 9 * 0.111....
= 9 * 1/9
=1
Why this is happening ?
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1 solution
That is not true. 0 . 1 1 1 … is exactly 9 1 . There is no approximation that is happening.
I have updated the answer choices.
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But how can 0.1111111111111111111111111111111........ infinite be exactly equal to 1/9 ? The number value is infinite so there is no sense that these two are exactly equal !
So, according to you if 0.1111111111......... is exactly equal to 1/9 then 0.99999999999....... is also exactly equal to 1. Then there is no point of discussion .
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Here's a pretty simple proof: We can actually rewrite 0 . 9 9 9 9 9 9 9 9 9 9 9 9 9 . . . or simply 0 . 9 as 1 0 9 + 1 0 0 9 + 1 0 0 0 9 + . . . = 1 0 9 + 1 0 2 9 + 1 0 3 9 + . . . This is a sum of geometric terms up to infinity, so we will use the formula, S ∞ = 1 − r a , − 1 < r < 1 where a is the first term in the progression and r is the common ratio between terms. Substituting a = 1 0 9 and r = 1 0 1 , we get 1 − 1 0 1 1 0 9 = 1 0 9 1 0 9 = 1 So, how can 0 . 9 9 9 . . . = 1 be false?
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@敬全 钟 – Yeah that's right.Thanks for the explanation .
@敬全 钟 – No, its approaching to 1 Not exactly equal to1, In your proof sum to infinite terms its approaching value not the exact value
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@Shiwang Gupta – We can write 0.111.....=1/9 Only if these ones ares are approaching to infinity. And if these are approaching to infinity than 0.999... is also approaching to 1
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@Shiwang Gupta – But the statement is still not true because it is approaching but not exactly equal to 1
0.111... is not exactly = 1/9 , So simply due to the approximation this is happening!