Unsurprisingly, an empire with a population of millions to tens of millions at various points in time did have a concept of a million. The actual way of writing it varied over time. The earliest system of larger numbers, carried over from the earlier Etruscan numeral system Roman numerals were adopted from, was the symbol for 1000, a straight line with a an arc curving from the top to each side, visually similar to the M that much later replaced it, but with additional pairs of legs, each added pair increasing the value by ten times, however this only went up to a 7 legged M representing 100,000, no records remain of a 9 legged figure for a 1,000,000.

At some later point, that system eventually evolved into the apostraphus notation. This was more or less the same, but instead of an awkwardly written M, it was instead split into multiple symbols, in which, for example, 1000 would be written as CIↃ, (that backwards C may or may not also have been a letter introduced to the alphabet by Claudius in the first century, I understand this is some dispute here). Additional bracketing C/Ↄ would, like before, continue to increase the value by 10 times, such as CCIↃↃ (10,000), CCCIↃↃↃ (100,000), and CCCCIↃↃↃↃ (1,000,000). Under both this system and the previous, half the value could be represented by omitting the left half, I've seen it proposed, though never conclusively, that this was how D (as a simplification of IↃ) came to represent 500.

But that's still a lot of writing to handle something as simple as a number, and scribes and bookkeepers needed something more efficient. Enter vinculum notation. It's a matter of some dispute as to when this started to be used and especially when it became the standard (it certainly existed by the first century AD, where it was used by Suetonius). In vinculum notation, numbers would have a bar written over them to indicate they are multiples of 1000, such as X̅ for 1000. This is, naturally, needlessly confusing, because it was already common practice to write bars over numbers to indicate that they were, in fact, numbers. The solution to this, theoretically, was to include a little flourish at the beginning and end of the line. Similarly, lines extending down from the bar, forming a sort of half-bracket) were used to indicate multiplying by 100,000 instead of merely 1,000. (X with such a line above and around it would then represent a million under this notation, and the bracketing lines extending fully to the bottom of the character would indicate multiplying by 1,000,000). This might seem needlessly confusing and likely to cause problems. And it did. Suetonius wrote in his Life of the Caesars of the case of Livia Drusilla, Augustus' widow, who upon her death willed a sum of money to a minor relation (who incidentally rose to became emperor some years later, but that's irrelevant here), written as CCCCC, with the overbar and half-brackets indicating a sum of 500,000 sesterces (125,000 denarii). However, the will was disputed and decided by Tiberius, who claimed that "quia notata non praescripta erat summa" (because the intended sum had not been written out in words), he had to award Galba the lesser figure of 500 sesterces. Although this may have had less to do with anybody being confused and more to do with Tiberius being Livia's residual heir.