What determines the value of fiat currency?

The value of Fiat currency is a nation's credit, and that is because it is used to clear off debt by the citizens of a nation.

Fiat currency is, thus, a government issued-currency that is not supported by physical commodity, such physical commodity can be gold or silver.

The value of fiat money then is gotten from the relationship between supply and demand and the stability of government issuing it instead of the worth of a commodity that backs it.

For example, the United states dollar, euro and many world currencies are all fiat currency.  

Government, historically, mint coins from valuable physical commodity and print paper money that could be redeemed for a particular amount of physical commodity.

In the case of inflation or hyperinflation, fiat money tends to loose value and this is because it is not connected to physical reserves such as gold or silver. if people lose faith in the country's currency, it tends to lose its value.

This is entirely different from currency that is backed by gold mainly because the demands for products made of gold such as jewelries, computers, electronic devices and aerospace vehicles are very high.

Fiat currency is issued by most government as legal tender for the purpose of debt repayment

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it was certainly a debatable decision, mainly because it was based primarily on political - and not on legal or social - views. since the congress at that time was led by members of the republican party, and the territory that the tribes wanted to turn into an exclusively indian state was predominantly democratic, the proposal (as expressed in the constitution) did not succeed, but the constitution itself proved to be of crucial importance in the creation of the state of oklahoma, and, most importantly, it guaranteed the involvement of representatives of the indian tribes in the government of the future joint state.  

as a member of congress, i would have voted to ratify the constitution, or at least to have it tabled. ignoring it was an interested and partial decision.