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I was reading a chemistry book and on the topic of how to round of measurements it said: "If the rightmost digit to be removed is $5$, then the preceding number is not changed if its even but is increased by $1$ if it is odd." But what is the reason behind such condition, I couldn't really find any reason anywhere can anyone help me with that?

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user45838
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    I know this as an IEEE standard. I don't really know why it's done but here's a place to start reading until a better answer comes around. https://en.m.wikipedia.org/wiki/IEEE_754#Rounding_rules – Sort of Damocles Feb 12 '18 at 14:07
  • It's to correct consistent rounding errors. If you always round down, all results would be too small, by mixing things up, you could hope that rounding errors cancel each other out. – Mathematician 42 Feb 12 '18 at 14:08
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    @Mathematician42 That depends entirely on what operation you do on them. If everything you do is add or multiply, then you're right, that would help to even things out. But if you subtract and divide, you would want to round everything in the same direction. – Arthur Feb 12 '18 at 14:09
  • @Arthur: You are right. Every such rounding rule will have its advantages and disadvantages, the basic idea here is to mix things up and hope for a good outcome. You can always find particular cases in which a certain rounding rule will give bad results. This particular rule just adds an almost random-like behaviour to rounding in both directions. It works as an idea. I'm sure there is study devoted to understanding rounding-techniques and their applications, but I don't think that's what the OP is after. – Mathematician 42 Feb 12 '18 at 14:15
  • You could see this question, which is a duplicate – Ross Millikan Feb 12 '18 at 14:33
  • What book is this? Are you sure that there isn't some condition saying that the number has to end in exactly 5 to round this way? – Thomas Feb 12 '18 at 15:21
  • @Thomas its NCERT chemistry part 1 for class 11th a standard book they use to teach in Indian schools, stuff about measurement is written very vaguely in the first chapter. – user45838 Feb 12 '18 at 15:27

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