When Some Currencies Appreciate, Others Depreciate

A news story once reported that the US dollar had risen 180% against the Yemeni Rial. Some people interpreted this as meaning that the Yemeni Rial had fallen 100% against the US Dollar.
That interpretation is wrong. If a currency falls by 100% against any other currency, the currency is worthless.
On the other hand, 100 Yemeni Rials could buy one US dollar, but can now buy only  
  US Dollar. The Yemeni Rial has depreciated by  
\[\frac{1-0.357}{1} \times 100 \%=64.3 \%\]
  against the US Dollar.

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