In all my time as a math teacher, I don't think there's been anything I've taught students quite as controversial as the idea that 0.999… repeating equals 1. Students just have an intuitive dislike of those symbols being set in equality with each other.

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In order to understand what mathematicians mean when they say that 0.9 repeating equals 1, we have to separate out three things: the value of a number, the process by which we generate that value, and the way we write that number down. For example, there are several different ways to write down the fraction 1/3. It could have come from 3/9 or 2/6. It could be expressed as 33 1/3 %. But the *value* of all those different ways to write it are the same.

Similarly, though point nine repeating is a kind of strange way to write down the value 1 (or 9/9 if you prefer), they are in fact the same thing. Though, to be fair, to have a proper 0.9 repeating equals 1 proof, you have to understand how sums of infinite series work, which typically doesn't happen until calculus. In calculus, though, we specify precisely what we mean by the sum of an infinite series and its convergence (or not). Until then, these recurring decimals are mainly an artifact of our decimal number system, and a consequence simply of how we choose to write numbers down, NOT fundamentally different values.

#point9repeatingis1 #repeatingdecimals #infiniteseries

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