together an example, the number 15, rounded come the nearest tens, ring to 20. I understand it"s arbitrary, as 10 and also 20 room equidistant from 15, I just wonder if there"s any kind of discernible reasonable behind the convention of round off up. Even something like, "It just feels much more natural", would certainly probably satisfy me. Just had to questioning :)

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reply Mar 21 "15 in ~ 20:48

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It isn"t always. A famous rounding technique called banker"s round off rounds 15 to 20 but 45 to 40.

You are watching: Round 15 to the nearest ten

But one factor it might be rounded that way is that round(x) is often applied as \$lfloor x+1/2 floor.\$

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reply Mar 5 "13 in ~ 21:41

CharlesCharles
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For tiny numbers choose \$15\$, it might feel closer come \$20\$. We have actually a specific (vague) logarithmic appreciation of numbers, so \$15\$ feel farther indigenous \$10\$ 보다 from \$20\$. Together the numbers get larger, this becomes much less important. Even \$25\$ doesn"t feel to me lot closer to \$30\$ 보다 \$20\$. Yet you have to do something. Occasionally you round to evens, which has the advantage of no accumulating errors if you add up a most them.

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reply Mar 5 "13 in ~ 21:44

Ross MillikanRoss Millikan
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Wikipedia does have a nice write-up on this problem. Expect it helps in any kind of way.

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reply Mar 5 "13 at 21:43

Mihai BujancaMihai Bujanca
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There is actually a handy reason for the dominion that we round up rather than down when we are exactly at the mid point, which counters the debate one normally hears that it is an arbitrarily choice. This is noted in Bradlee"s answer but I"m posting among my very own to expand on it.

Take the the following three numbers that we want to round to 1 decimal place:

0.1490.1500.151In the case of 0.149 we only ever need come look at the percentage percent place. It makes no difference what appears to the ideal of that because the number will constantly be smaller sized than 0.15, so we recognize from looking in ~ that place alone that we will certainly round down to 0.1.

With 0.150 and also 0.151, we look in ~ the percentage percent place and see we have a 5. There space two possibilities for what might show up in the areas to the right: all zeroes, or a non-zero digit. If it"s all zeroes, we round up to 0.2 because of the rule. If over there is a non-zero digit, then we round up, since the number is greater than 0.15. Either method we round up, which means that we don"t actually should bother feather at any kind of places come the appropriate of the hundredths place to identify our action.

What if the rule was that we round down? In the instance of 0.149, us still only must look in ~ the hundredths ar for the same reason as above. With 0.150 and also 0.151 though, looking in ~ the hundredths ar isn"t great enough. If the locations to the right of it space all zeroes then we will need to round down to 0.1 due to the fact that of the rule, however if over there is a non-zero digit then we will have to round up due to the fact that it is greater than 0.15. Due to the fact that there are two possibilities, we have to actually check.

With a round off up rule we have one procedure that works for all cases: look at the place to the best of the one you space rounding to. V a round off down rule we require a one-of-a-kind procedure as soon as we uncover a 5 in that place: examine each place to the appropriate until friend either reach the finish of the number or discover a non-zero.

See more: How Many Different Arrangements Of 5 Letters Can Be Made From The 26 Letters Of The Alphabet?

Note the this logic doesn"t use to an adverse numbers however unless you invert the rule (i.e. Round down for the digit 5 in a an unfavorable number).