Although Fibonacci covered an entire realm of mathematics, the main numbers used in trading are actually percentages. The percentages are 38.2%, 50%, and 61.8%. These areas are viewed as trend retracement points. The most commonly held theory is that a 38.2% retracement of a trend is a failed reversal and the overall trend should continue. A retracement to the 61.8% mark signals that the retracement is the beginning of a new trend. The 50% level is used for different strategies if confirmed by several other signals
The use of Fibonacci numbers in trading has become increasingly popular in recent years. It does not take long when looking at charts to see several examples of Fibonacci tracements. On numerous occasions I have watched analysts making market predictions on T.V. shows. I will often check the charts about what they discussed. Some of the predictions for new price levels are dead on Fib. retracement numbers.
Fibonacci numbers, as with all technical indicators should not be used by themselves. They should be combined with other indicators to make a complete system to trade with. I do believe that Fibonacci numbers should be a part every traders list of indicators. They do seem to be extremely accurate, This could possibly a self fufilling prophecy. If enough people believe it, they will cause it to hold true.
In any case, if you do not currently use them, you may want to look into it.