Saying 10 but meaning 10,000 in Latin

Question

In Petronius we find reference to a cloak which they say literally costs 10 sesterces but I think what they're doing is the same practice in English where if I ask you how much did your car cost and your respond 15, the listener is expected to understand that you mean 15,000. Here is the actual passage:

subducta enim sibi vestimenta dispensatoris in balneo, quae vix fuissent decem sestertiorum.

And later we learn that it is Tyrian purple which was presumably a luxury item.

Tyria sine dubio, sed iam semel lota

In the excellent commentary on the Satyricon by Schmelling we find:

X = decem milia, M. Smith (1975), Oberg (1999), Schmeling: decern HL, Maller (1961+) sestertiorum. Smith argues that X is an absurd figure but more appropriate to the context as a deliberate exaggeration (especially after vix at 17.9). HS 10,000 as the price for a cloak is mentioned by Martial 4. 61. 4-5.

And later:

In Suetonius Nero notes that Nero forbade (as a trick) the use of Tyrian purple dyes. This suggests that the correct reading at §8 is HS 10.000.

I just want to make sure that what is going on here is that they are abbreviating the number from 10,000 to 10 and you're just expected to know that, not that there is some other way to infer the correct number such as sesterces being in the genitive case.

Answer 1

The first question is what is the case usage of "decem" in "decem sestertiorum." It looks like a genitive, but is this possible with a specific price, or is this casual reference enough to make it non-specific? Is it a genitive of value?

If the case of decem is fundamentally a genitive, then the underlying form of the phrase may be decem sestertia, with sestertiorum used as a rare genitive plural instead of the usual sestertium.

According to Lewis & Short, Wiktionary, and Oxford's Latin Grammar:

For 2000 to 1,000,000 sesterces, you use sestertia as a pluralum tantum adjective modifying the understood word milia, but you normally count with the distributive numerals, rather than the plural tantum numerals.

With respect to the use of cardinal numbers instead of distributive numerals, Lewis & Short say:

Rarely with card. numerals: “sestertia centum,” Sall. C. 30, 6: “septem donat sestertia,” Hor. Ep. 1, 7, 80: “centum sestertia,” Mart. 6, 20, 1: “sex sestertia,” id. 6, 30, 1;

It would seem then that decem sestertia = dena sestertia = dena milia sestertia = ten thousand sesterces and that decem sestertiorum is a genetive of value or something similar.