The relative value of currency isn’t actually that good a metric of its worth. It tends to correlate because of you have a ton of inflation, as you often see in failing economies, then your exchange rate gets really high. But the Yen, from what I recall, is pretty close to being the US cent. So a $3 thing might be 300 Yen, but a $10/hour wage would be 1,000 Yen, say. So it all works out about the same.
You’re looking at it the wrong way. The denomination of the currency doesn’t matter nearly as much as how much purchasing power an equivalent amount of another currency represents. One way to look at it is the [Big Mac index](https://en.m.wikipedia.org/wiki/Big_Mac_Index) which measures how many burgers you could buy for $50US in various countries. 1USD is worth roughly 100JPY which will buy you approximately the same amount of goods and services in either country.
Japan had a lot of inflation post WWII because their economy was shit because their country got bombed to fuck.
Most countries that experience a lot of inflation switch their currency at some point so the numbers aren’t so huge.
In the last 100 years, Germany has had German Papiermark, Reichsmark, Deutsche Mark and Euro.
Japan on the other had, instead of creating a new currency with new denominations, they just said ‘meh, deal with it’. Got rid of their ‘penny’ equivalent. And just had bigger numbers.
Say you have a cake and I have a cake. Each cake represents the size of our economies and they are equal.
I decide to cut my cake into 4 pieces, you decide to cut yours into 16. Our economies haven’t changed and you are neither richer nor poorer.
Nevertheless, if we decide to exchange slices, I will expect 4 slices of your cake in return for one of mine. That is only fair since your slices are smaller. This is the exchange rate. It says nothing about who has the biggest cake or best economy. It just shows that one of your slices is a smaller proportion of your overall economy than mine is of my economy.
So it is with Japan and the USA. The Yen appears to be “worthless” simply because it is a much smaller slice of Japan’s economy than the dollar is of the US’s.
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