In economics, we learned about appreciation and deappreciation of currency and the 2 types of exchange rate systems. But I still do not fully understand how a currency has value vs a fake one or how a currency changes value in different business cycles?

I hope that I do not sound too stupid about this.

I just really want to get into the nitty-gritty of this to understand the rationale when it comes to value in currencies.

I understood that fixed exchange rate is controlled by the government while the floating exchange rate is basically regulated by itself so basically, the system of the stock market will automatically balance itself based on the supply and demand of the currency

And I understood that a currency will appreciate when there is an inflation which will make exports more expensive, interest rates more expensive and therefore, the inflation will decrease.

The opposite goes for deappreciation in a recession in order to incentivise more spending and borrowing.

However, the thing that I really do not understand is the HOW of the process that gives the value of a currency.

If there is not a number written on the paper money, it would simply be a random paper money where the value could be anything.

But how is that value given and accepted and recognised everywhere as legit versus a currency that is fake or old or too new to be accepted?

(like how is crypocurrency really considered as valuable by some or not valuable or real by others, even if the person does not understand what that value means like an x amount of crypocurrency means y amount of dollars?)

What gives money value? How is it given?

And how come the value of a currency changes in different business cycle, while also, different currencies require certain amount of exchange rates to keep the value of 1 of x amount of money equal with the other currency?

To try to evaluate what I mean by the confusion, I am going to try to use math and physics.

If I have a piece of chocolate that weighs a 100g, it will stay a 100g unless I eat some of it or add some chocolate on top of it

And yes, I understand that SI unit of weight which is in grams, it is technically man-made and the metric system is meant to be divided by periods of 10, while the imperial system should technically be the same weight but from a different value.

So, while I do not fully understand how the SI unit of grams is made so accurately to make sure that the weight is correct, what I can say that 100g of chocolate stays 100g of chocolate.

But if I have a 100 dollar bill, where did the value of the 100 dollars come from, regardless of whether the number 100 is written on it or not?

How is the value given and even accepted by all the bankers and financial advisors and accountants and think that this 100 dollar bill is real and not 90 dollars?

And how come a 100 dollar bill will lose or increase its value in different business cycles, even though the number of dollars on the bill still says a 100 dollars?

Why would a 100 US dollars equate to an x amount of Euros or Yen instead of being 1 to 1?

How is it possible that the value increases or decreases that everyone accepts it?

And even though the exchange rate is either fixed or floating, who exactly has the power to change the value into that exact amount and how will they know that the value is exactly correct?