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A round number is defined, informally, as one with lots of zeroes at the end, or one that ends with a 5 (perhaps because it's easier to give change to). What would you call a number that wasn't "round" in this way?

I'm less interested in the mathematical definition (where a number has considerably more and smaller factors than its neighbours). For example, consider 1000 to be a "rounder" number than 1024.

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I always thought a round number was one that had been rounded, and therefore a number that has not been rounded is an exact number. –  Jim Nov 7 '13 at 4:41
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The WP definition is not quite what you made it out to be here :) Also note that a round number is a 'low precision' representation of a 'higher precision' value. Strictly speaking, zero and five are not relevant. –  Kris Nov 7 '13 at 5:15
    
You asked about an informal definition; so I'll offer an informal antonym: an odd number. Mathematicians may bristle, saying any number that isn't even is odd. But consider your change example: I like when my total at the register comes out to a nice round number, but don't like it when it comes out to an odd number. In other words, I like it when my lunch costs a nice "round" $5.75, rather than an "odd" $5.76, where I'll have to carry six coins in my pocket, instead of just one (although I might be more inclined to call that an odd amount, as opposed to an odd number). –  J.R. Nov 7 '13 at 14:52

3 Answers 3

up vote 3 down vote accepted

Your presumed definition of a 'round number' is only partly correct. Consider this:

1000 is a "rounder" number than 1024.

Also:

1020 is a "rounder" number than 1024.

However,

1000 is a "rounder" number than 1020.

In other words, 1000 and 1020 are both obtained by 'rounding' off 1024. Therefore, a number's 'roundness' is based on two factors: that which it is rounding and the degree to which it is rounding off.

A 'rounded-off' number is the result of an original number being operated upon. The original number cannot be 'defined' (or named) in terms of what it may be rounded into from time to time.


In absolute terms, (see above) one could call such a number a
sharp number

n. A precise or unrounded number.
… Round numbers have a salient conceptual basis (e.g., 10 years are a decade). Sharp numbers do not (e.g., 7 years). Estimates tend to be expressed with round numbers. An experiment is described that examines whether consumers make the false assumption that claims using sharp numbers are less likely to be estimates (i.e., are more factual) than those using round numbers and, if so, whether this makes sharp-number claims more believable. The results demonstrate that such assumptions do occur, particularly for those consumers considered to be advertising skeptics. —Robert M. Schindler, Richard F. Yalch, "It Seems Factual, But Is It? Effects of Using Sharp Versus Round Numbers in Advertising Claims," Association for Consumer Research, October 1, 2005

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According to OP, I think that 1200 is a rounder number than 901 because it has more zeroes in it. It clearly states that he is not interested in mathematical justifications. I will still give a +1 for 'sharp number'. –  Fr0zenFyr Nov 7 '13 at 5:44
    
@Fr0zenFyr "1200 is a rounder number than 901" even for me, in a given context, but not otherwise. –  Kris Nov 7 '13 at 5:47
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Sharp number seems like a good, precise definition. I disagree that round numbers imply that they were rounded from something; sometimes you can come up with numbers that were round to begin with. –  congusbongus Nov 7 '13 at 6:55
    
@congusbongus How 'round' can a number be? A number is always 'round' in a relative sense. Is 7000 a round number? Quick, answer it without applying additional logic. :) –  Kris Nov 7 '13 at 12:48
    
It's not the O.P.'s "presumed definition" of a round number, though, it's the definition linked to in Wikipedia: a round number is informally considered to be an integer that ends with one or more zeroes (0), such as 1,000, 1,500,000, etc., and a number ending in 5 might be considered in a way more "round" than one ending in neither 0 nor 5. Even a non-integer such as 2.5 might be seen as more round than, say, 2.497. But that confirms what you say about numbers always being round in a relative way. –  J.R. Nov 7 '13 at 13:40

The opposite of a round number is an exact number. The meaning is literal. When someone talks about round numbers, they usually are implying they are not exact.

You may also be familiar with the terms precise number and accurate number. A common expression is "accurate to X digits", meaning only X digits are correct, and the other digits have been "rounded". "Precise" can be used in a similar way. In other words, a rounded number can be accurate (or precise) with some describable error. It may be accurate or precise (to within some specified of stated error), but it's still a round number. It's not exact.

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But numbers can be both exact and round, especially in contexts where people expect round numbers. For example I can say "I bought this doodad for exactly $500"; 500 in this case is both exact and round. –  congusbongus Nov 7 '13 at 5:01
    
You're right. All numbers can be considered exact. That's why I put the word "usually". I don't think you're going to find a single term that is commonly used to express "not round". Even the link provided by Safira to "non rounded" equates it to a "sharp" or "precise" value. But all numbers are precise in the same sense they are exact - both rounded and "non rounded" numbers. –  Canis Lupus Nov 7 '13 at 5:28
    
+1 for "precise". –  Charles Nov 7 '13 at 6:20

It's a non-round number, I found it in here.

It's a number that has a sharp or precise numeric value; has not been "rounded".

The simple understanding is that the opposite of something is every other thing that is not included as that something or has no such characteristic that something has in common. Therefore, for things like this (that have no special names for their opposites), putting a word non preceding it might not be a bad idea.

You can use this for any other kind of number. Like integer. This says that round numbers originate from integers that end with one or more zeroes. The opposite of an integer is any number that is not an integer (non-integer).

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