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.?

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.

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 \(\displaystyle \large 9 \cdot \sum_{n=1}^ \infty \frac{1}{10^n}\)

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TopNewest\(0.99999...\) and \(1\) are exactly the same. See this previous post.

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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.

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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 \(\displaystyle \large 9 \cdot \sum_{n=1}^ \infty \frac{1}{10^n}\)

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