Why .9 repeating equals 1

The zeros are also infinite, there is no 1 at the end. There is no "end", there will also be another 9 or another 0. Since any number subtracted from an equal value is zero:. Math Wiki Explore. Browse content. Register Don't have an account? Proof:The Decimal 0.

View source. History Talk 0. See also the Wikipedia article: 0. Categories Proofs. Fan Feed 1 Tetrahedral number. You'll get an infinite string of zeroes. The zeroes go on forever. And 0. Argument from philosophy: If two numbers are different, then you can fit another number between them, such as their average.

But what number could you possibly fit between 0. Argument from algebra: The expression 0. Call this numerical value " x ", so 0. Multiply this equation by ten:. There is no "end" after which to put that zero. Argument from semantics: A common objection is that, while 0. But what is meant by "gets arbitrarily close"? It's not like the number is moving at all; it is what it is, and it just sits there, looking at you.

It doesn't "come" or "go" or "move" or "get close" to anything. On the other hand, the terms of the associated sequence, 0. No matter how small you want that difference to be, I can find a term where the difference is even smaller.

This "getting arbitrarily close" process refers to something called "limits". You'll learn about limits later, probably in calculus. And, according to limit theory, "getting arbitrarily close" means that they're equal: 0. Note regarding all of the above: To a certain extent, each of these arguments depends on a basic foundational doctrine of mathematics called "The Axiom of Choice". Something similar happens with irrational numbers that have non-repeating decimal expansions.

In general, any infinitely long decimal expansion is thought of as the limit of the sequence of terminating decimals that make up the infinite expansion. So, the reason why 0. For you. World globe An icon of the world globe, indicating different international options. Get the Insider App. Click here to learn more.

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