From Paul Goldenberg, a commentary on “units digit” versus “ones digit”

After a brief conversation, Paul Goldenberg, lead author of EDC’s Think Math! curriculum, had this to say on the debate between the phrases “units digit” and “ones digit”.

Yes, anything can be a unit.  There are lots of arguments one could make either way, I suppose.

A simple case for “ones” is that it is more parallel to “tens” and “tenths” — a specific magnitude named after a specific number.

The number 1 (ok, and –1) is, of course, a “unit” (in the world we care about) but that’s a different use of the word. Unity and oneness are also, though synonymous, slightly different uses than the number-name “one.”  CCSS chooses to call teen numbers “one ten and some extra ones.” It feels slightly weirder to say “one ten and some extra units” but only (again) because of the not-quite-parallel language. And, educationally, “one” is a more familiar word than “unit.”

There!  I’ve defended “one” about as much as I can.  But is that a case for “ones digit” over “units digit”?  Only the “familiarity” argument honestly holds any weight with me, and not much weight.  After all, the idea of choosing a unit and basing everything else on that unit seems valuable, and “1” is the obvious candidate in the integers. When we’re measuring distance between cities (in any sensible country), we definitely choose km and not m as the purpose-specific unit but the entire naming system is based on m as The Unit (km and cm are just modifications of m).

Hmm, so maybe 10 should be the unit in the integers, since our decimal (that’s its name) system is based on powers of 10.  So there! I’ve wound up defending “one” a bit more by showing how slippery “unit” can be.

I’m actually not sure what led to the choice of “units digit” for all of Think Math, but I do know why we chose the symbol u to label that column (because I had to answer it many times, which might well have been the source of the naming we chose): o looks too much like 0.

Is there a strong case to be made against “units digit,” given the various ambiguities we get for either choice?  I’m not convinced there’s anything mathematical in this discussion, since the meanings of any of these terms depends so much on context.  After all, in the numeral 235, the two’s place is in the hundreds’ place. (Oh, should those have apostrophes or not?) Pedagogically, I’m convinced that it doesn’t matter at all.  Oh, and one more argument for “ones digit” (or ones’ digit): if vast majority usage goes one way, then bucking the usage is ornery and unhelpful.  But, sigh, there are so many places to put one’s (or unit’s) energy.  I can’t get worked up much about this unit.


About Bowen Kerins
Bowen is a mathematics curriculum writer. He is a lead author of CME Project, a high school curriculum focused on mathematical habits of mind, and part of the author team of the Illustrative Mathematics curriculum series. Bowen leads professional development nationally, primarily on how math content can be taught with a focus on higher-level goals. Bowen is also a champion pinball player and once won $1,000 for knowing the number of degrees in a right angle.

One Response to From Paul Goldenberg, a commentary on “units digit” versus “ones digit”

  1. Tim Dynan says:

    Hi, I’ve always been swayed towards units because once you introduce fractions it makes more sense to students. For example, we say all fractions are part of a whole. But a whole what? – Students get really mixed up on that word (eg whole, hole, etc). I say a fraction is a part of a whole unit, then the link is made to the place value system.

    If you used the word ones you’d be saying part of a whole one, or I now have one whole one which I don’t think helps.

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