The US Dollar is declining in value against the British Pound and the Euro, but the decline versus the Euro is greater.
If US interest rates are reset lower, I am told that the value of the Dollar versus the other currencies declines further.
These exchange rates are calculated to four decimal places, indicating significant precision.
If the Chinese Yuan is set higher than it currently is, what will that do to the Dollar versus the Pound and the Euro?

Answer
Exchange rates are not calculated the are determined by the currency exchange markets where traders by and sell currencies. see FOREX.
The theory predicts that that the demand for dollars is dependent on the interest investors can get on dollar denominated bonds, so a lower interest rate decreases the demand and would lower the "price" of the dollar, but the amount of the decrease is a rough estimate.

How do people figure out the currency exchange rate?

Seriously? How do they figure this out?
I calculated the currency exchange for a bag of chips in India which were for 10 rupees, and that was like 21 cents in the USA. Let me just say that the potato chips bag was medium sized.

Answer
Like many other things in economics, supply and demand of the foreign currency will determine the exchange rate in the foreign exchange market (or the equilibrium, aka the spot exchange rate). Supply and demand are constantly fluctuating which is why the spot exchange rate (equilibrium in the ForEx market) is always fluctuating.
So, it's not people that figure out the exchange rate, it's the foreign exchange market :)