The need to exchange currencies is the primary reason why the forex market is the largest, most liquid financial market in the world. It dwarfs other markets in size, even the stock market, with an average traded value of around U.S. $2,000 billion per day. (The total volume changes all the time, but as of August 2012, the Bank for International Settlements (BIS) reported that the forex market traded in excess of U.S. $4.9 trillion per day.)
For trading purposes, the first currency listed in the pair is always the directional currency on a forex price chart. If you pull up a chart of the EUR/USD, and the price is moving higher, it means the EUR is moving higher relative to the USD. If the price on the chart is falling, then the EUR is declining in value relative to the USD. The attached chart shows this. 

One unique aspect of this international market is that there is no central marketplace for foreign exchange. Rather, currency trading is conducted electronically over-the-counter (OTC), which means that all transactions occur via computer networks between traders around the world, rather than on one centralized exchange. The market is open 24 hours a day, five and a half days a week, and currencies are traded worldwide in the major financial centers of London, New York, Tokyo, Zurich, Frankfurt, Hong Kong, Singapore, Paris and Sydney - across almost every time zone. This means that when the trading day in the U.S. ends, the forex market begins anew in Tokyo and Hong Kong. As such, the forex market can be extremely active any time of the day, with price quotes changing constantly.
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