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

December 2, 2014 Leave a comment

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.