Why is the dollar today worth about 45 cents?

The dollar is, by definition, worth 100 cents. However, the value of the dollar changes over time due to inflation (or more rarely, deflation) and there are also different dollars in different countries, for example, the US dollar and the Canadian dollar, which do not have exactly the same value.

If you are refering to the value of the coin's composite metals then please state it in the question.