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Since the *10* and *19* represent the year of the emperor's reign how do you know which era they belong to when determining the date?
That can sometimes be tricky!
In the case of your meter stamps, it's pretty easy, because they also have the last two digits of the year in the Western calendar on them. The Isaji meter has *10* and 98 on it, and since Heisei 10 = 1998, there's no difficulty. Similarly, the Iwade meter has *19* and 07, and Heisei 19 = 2007. Both of those meter stamps have the date in the usual Japanese order: year-month-day.
Some of Rod's examples, however, have the date in Western order (day-month-year). When it's something like 08.03.94, it's obvious that 94 is the year, since no month has 94 days in it. But when it's something like 01.12.06, it's trickier, because the year could be either 2001 or 2006. But since the meter stamp with the date 01.12.06 has *18* on it, that can help you figure it out.
Heisei 18 = 2006, so the date is 1 December 2006.
When dealing with postmarks on Japanese stamps or covers, however, you'll normally only have a Japanese era year and no Western year to help you out. This usually isn't too much of a problem, because Shôwa was such a long era. You can usually tell pretty easily whether something with the year 5 on it looks like it came from Heisei 5 (1993) rather than Shôwa 5 (1930). As we progress further into the Reiwa era, it may become more difficult to differentiate between a Heisei date and a Reiwa date, but we're only in the first year of the Reiwa era right now.
Older stuff can be trickier. It may be obvious that something with the year 5 is much too old to be Heisei 5 (1993), but is it from Shôwa 5 (1930) or Taishô 5 (1916)? Here you would need to look for other clues. Does the cover have a Western date on it somewhere, such as a receiving postmark from another country? If not, you may need to look up the stamp(s) in a catalog.
Case in point: I have a Japanese cover with a postmark of 5.1.9 on it. It looks like it's from before World War II, so I can safely rule out Heisei. I determine that the stamps are Scott numbers 131b, 133, and 194. Since #194 wasn't issued until 1926, that rules out Meiji and Taishô (1926 was Taishô 16 and Shôwa 1). So the year 5 in the postmark must be Shôwa 5 (1930).
Coin collectors don't have this problem. Japanese coins have both the name of the era and the year on them.