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  
\[\frac{100}{280}=0.357\]
  US Dollar. The Yemeni Rial has depreciated by  
\[\frac{1-0.357}{1} \times 100 \%=64.3 \%\]
  against the US Dollar.