# Use of an Apostrophe in Maths Place Values

In mathematics, when you're discussing the concepts behind different number bases, it's often necessary to refer to a digit's place. For example, in the following "base 10" number (the number system most people normally use)

``````217
``````

you'd say

There's a `2` in the hundreds place, a `1` in the tens place, and a `7` in the ones place

However, I'm uncertain where, (if at all), I should use a possessive apostrophe.

• `2` in the hundreds place
• `2` in the hundred's place
• `2` in the hundreds' place

This seems like the perfect intersection of mathematics making up terms and debates about possessive apostrophes and plurals. Is there a general rule or consensus for this sort of usage?

• Opinions among writers and grammarians differ on whether to use an apostrophe, however many sources are against both systematic use and systematic avoidance of it, especially in your latter case. – user51029 Sep 13 '13 at 22:17
• An argument could be made for both hundreds and hundreds' but not for the hundred's. The latter indicates there is a specific 'hundred' and this is its place. – terdon Sep 13 '13 at 23:09
• At some point don't things like this just morph into the simple form by way of long usage ? E.g., Middle English to morow morphed from the Old English to morgenne (which I'm guessing is some derivation of German Morgan) and similar today from to-day etc. So things like apostrophes which might just seem irksome get dropped off after a while ? Just curious, I looked through a bunch of math books (I have a ton) all six I found that contain number systems place holders use "ones" "tens" "hundreds" sans the apostrophe. – Howard Pautz Sep 14 '13 at 0:23
• Well, according to this Tom Lehrer himself did not use the apostrophes and I will accept no higher authority than he! – terdon Sep 14 '13 at 1:46
• @terdon LOL that was a fun read. Thx. Sure wish I had had him for a math teacher! – Howard Pautz Sep 14 '13 at 2:00

Although perhaps not as authoritative as Tom Lehrer (See terdon's comment under OP ), here are some examples from text books:

" Place value - [...] a particular position in a place-value notation, for example, units, tens, hundreds [...] " 1)

And, though referring to the right side of the decimal place:

" Decimal - [...] The first position to the right of the point (representing tenths) is [...] A decimal fraction is [...] a number of tenths, plus a number of hundredths, plus a number of thousands, etc. [...]" 2)

And from a much older dictionary my father had (for which he paid a whopping USD \$0.60 [ah, that'd be six tenths of a dollar :-P ] ), we have:

"Decimal System - [...] 20,349 = 9 units + 4 tens + 3 hundreds + 0 thousands + 2 tenthousands. [...]" 3)

[Interesting, the editor parser flags "tenthousands" and offers tries to pull it apart to 'ten thousand' or hyphenate to ten-thousands. I guess our dear SE. programmers have not read reference #3. ]

[EDIT - clarification based on side discussions]

The problem, or confusion here is that these units (tens, hundreds, etc.) can be singular or plural units (similar to Fish), but also can be like adjectives. Perhaps a linguist can chime in here with the correct term (quantifier adjective, a "naming noun" (see below) ?).

So, consider that

2 in the hundreds place

is exactly the same structure as

2 in the red place

We'd never say "2 in the red's place" - red is not a noun, neither is "hundreds" here. The units are labels modifying "place". What place? The hundreds place. The hundreds go in that place, but they don't possess it.

Consider it another but similar way. I have two boxes, one red, one blue. And I have a bunch of marbles. I'd say "I put 2 marbles in the red box and 4 in the blue [box]" I'd never say "marbles in the box belonging to red, " likewise not "marbles in red's box."

It's the same with hundreds - we put 2 units of something into the place holder which has these unit labels attached. Part of the confusion is that they all end in "s" ... so I would not be surprised if an author were tempted to think them as nouns, but I have not seen it yet.

Does that make sense?

[EDIT 16 SEPT 13 Found another reference. Though just a blog, it gives a nice simple answer.]

First and foremost, the apostrophe should NEVER EVER EVER be used to show a plural (that is, any naming word [a noun] with –s on the end). For example, noodles, chocolates, flowers. This is also true of numbers and dates – tens, hundreds, thousands (10s, 100s, 1000s; 60s, 1840s, etc.).

The –s is added to show that there is more than one of that particular thing, end of. No apostrophe needed, thanks.

The ONLY time you add an apostrophe to a plural noun is if you’re showing possession. [...] 4)

Note that the so-called debate ( which I was called out on :)) stemmed from thinking the units, tens, etc were possessive nouns modifying "place", i.e., "the ten's (or tens') place." This makes as much sense as "the red's box" or stranger, "the reds' box". Clearly, the problem arrises because of the words ending in S.

One final phrase which I hope will make this answer canonical enough:

The places where the units, tens, and hundreds go.

(They don't own those places :))

References:

1) Harper Collins Dictionary of Mathematics, New York, 1991. pg. 450

2) Penguin Dictionary of Mathematics, London, 1989. pg. 104

3) The Universal Encyclopedia of Mathematics, New American Library of Literature, New York, 1964, pg. 163

• It would be better to create a canonical answer rather than simply place an addendum at the end. It doesn't matter if edits occur all the way through: the history is retained. – Andrew Leach Sep 14 '13 at 10:19
• A canonical answer is THE answer to a question, correct and complete in itself. – Andrew Leach Sep 14 '13 at 14:39

think why there is an S at the end of the unit name at all. it is not to pluralize. why would you pluralize it? what does pluralizing it get you? nothing. you can't look to mathematicians for proper grammar. it is the ones' place. prove that it isn't. if there is a house that belongs to multiple people the Robinsons, you don't call their house the (plural) Robinsons house. that's retarded. you call it the Robinsons' house (if you mean that they ALL own it together, not just one guy named Robinson, as the ones and tens do. all ones own the ones' place, so they go there/ the places are designated places branching out from the decimal point. please end this argument. it is PLURAL POSSESIVE

~ ONES' PLACE ~ ~ TENS' PLACE ~

if you have any understanding of the concept you know it is this way. Howard Pautz's answer is wrong.

• Welcome to EL&U. Note, this site is different from others: it's not a forum. An answer on this site is expected to be authoritative rather than merely offering an opinion. You can edit your answer to add references to support your view, as well as updating it with standard English orthography. For further guidance, see How to Answer and take the EL&U Tour :-) – Chappo Dec 23 '18 at 8:16
• "Ones" or "tens" is merely the label assigned to the bin. Labels relate to organizing structure, not the content being organised. We don't typically treat those as genitives. You don't rent a subcompact's car. And you don't reference the tens' place. – Phil Sweet Dec 23 '18 at 13:58