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Does $2.4\overline{9}$ round to $2$ or $3$ when rounded to the nearest whole number? When rounding to one digit, we generally only take the first decimal space, which in this case is $4$. So on that front, it should round to $2$. However, $2.4999$... is in essence $2.5$, which will round to $3$. In this scenario, should the number round to $2$ or $3$? Thanks for your clarifications.

Landuros
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Lithanium
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    $2.4\overline{9}$ is not 'in essence' $2.5$, it is $2.5$. – Landuros Apr 06 '23 at 01:42
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    There are multiple, differing conventions on which way to round a half-integer, depending on what situation you're in (check the "Rounding" article on Wikipedia if you'd like). It's hard to figure out what your specific situation might be, as you seem to be able to keep around an infinite number of digits. – JonathanZ Apr 06 '23 at 01:53
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    Q: Does 2.4999... round to 2 or 3? A: Yes. – uhoh Apr 06 '23 at 05:18
  • This question seems more a computer science question. The number 2.5 is exactly in the middle of 2 and 3. Deciding how to round it is not a mathematical question, it's a computer science convention depending on your particular needs (round up, down, to nearest even number, etc). – PatrickR Apr 07 '23 at 04:53

2 Answers2

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When rounding to one digit, we generally only take the first decimal space, which in this case is $4.$

This applies only when the decimal representation is not a recurring decimal.

$2.4999$... is in essence $2.5$

$2.4999$... is precisely $2.5,$ so rounds to the same number as $2.5.$

ryang
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2.4999.. is not in essence 2.5. Because there is no number between 2.4999.. and 2.5, they are the same number. Therefore, 2.4999.. rounds to three.

Baimee
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