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We know \(3 \times \frac{1}{3} = 1\) which can also be written as \(3 \times 0.33333.... = 0.9999999... \neq 1.\).Why this happens, why both are unequal.?

Note by Kishan K
4 years ago

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\(0.99999...\) and \(1\) are exactly the same. See this previous post. Tim Vermeulen · 4 years ago

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How can you confirm that 1/3 = 0.333333.... It is not exact value it is just the approximate value that we use at our convenience when needed. As approximation is taken approximate value is obtained that is 0.99999.... not 1. Shubham Kumar · 4 years ago

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The difference between \(0.9999 \ldots\) and \(1\) is infinitesimally small. As such we can't really tell\see the difference between them.

They are actually equal. You can also prove this by an infinite geometric progression which is of the form \(\displaystyle \large 9 \cdot \sum_{n=1}^ \infty \frac{1}{10^n}\) Aditya Parson · 4 years ago

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