Does it mean the company pays 3% of the total earnings to the stock holders? So if I have a stock that has 1$ EPS I would receive 3 cents?
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It means a 3% return on the value of the stock. If a stock has a $10 share price, the dividend would be $0.30.
Normally though, the dividends are announced as a fixed amount per share, because the share price fluctuates. If a percentage were announced, then the final cost would not be known as the share priced could change radically before the dividend date.

Benjamin Chambers
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Clarification - aren't dividends stated and issued quarterly? e.g. A $1 dividend per year announced as $.25. – JTP - Apologise to Monica Nov 03 '11 at 16:23
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2There can be any number of dividends per year, but typical practice is four quarterly dividends of equal amounts. The yield, which is what "a dividend of 3%" is called, is always given as an annual percentage of the current price. Since the price fluctuates daily, the yield (dividend percentage) also fluctuates daily. – mgkrebbs Nov 03 '11 at 19:14
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@mgkrebbs actually that depends on the county and company 2 dividends a year is common in the UK- its only some of the big Investment trusts that do quarterly – Pepone May 06 '15 at 22:45