Didn't Coin World do an article on this recently? The lowest-value coins from Rome were the quadrans. They were 1/64th of a denarius.
In absolute terms, the Rin was not worth as little as that. It last minted in 1892, when the yen was 26.96gm (about 1oz) of silver, or equal to a Morgan dollar. 1 sen was 1/100 of a yen, or equal to one cent. So with 10 rin to the sen, the rin was equal to about 1/10 of a US cent. Still small, but not $0.000095, more like around $0.001
Japan was one of the few "dollar" economies to make a 1/1,000th unit a viable reality, although all coins below 1 yen were demonetized in 1953: https://www.boj.or.jp/en/announcements/education/oshiete/money/c07.htm/ The yen was fixed to the USD under the Bretton Woods system at 1:360, thus a rin was technically worth 0.000278 of a US cent between 1949-1953, although the lowest to actually circulate was the 50 sen coin, worth .14 US cent then, or a few cents today. Better yet, when Japan was transitioning from the Tokugawa monetary system to the new Yen, from 1870-1877 the old currency could be exchanged for new at the rate of 1 Ryo = 1 Yen, thus you needed 4 Mon coins to exchange for a rin