0.9 recurring is 1

0.999… is the same number as 1. It’s counterintuitive, but mathematics says that it’s true. Whether you believe it or not is another matter.

0.9 recurring
File:999 Perspective.png: Melchoir, AzaToth, Mets501, Sopoforic derivative work Pbroks13 [CC BY-SA 3.0], via Wikimedia Commons
Mathematics and statistics are full of counterintuitive results: common sense tells you something different, and common sense is wrong. One famous example is the Monty Hall problem – I had a long argument with my math teacher and friends about that one!

I’m not even going to try to summarise all of the proofs and arguments for this result. The one I find most convincing is this:

x = 0.999…
10x = 9.999…
10x = 9 + x
9x = 9
x = 1

One Reply to “0.9 recurring is 1”

  1. The main difficulty people have with this is the issue of whether a number could have more than one name. Usually I get people to first admit that 1/2 = 3/6 and that doesn’t bother them. Then 0 = -0. Then, in the decimal system, most numbers have a unique decimal expansion but the very rare weirdos A / 10^B have two, and it’s not a big deal.

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