Why are the seventy weeks (literally seventy "sevens") correctly interpreted as seventy weeks of years, i.e. 70 times 7 years, or 490 years? It is because of the following three important ideas with which Daniel's audience would be very familiar.
The first idea is that the Babylonian captivity was a punishment (Jeremiah 25:4-11). The second is the concept of an original punishment being multiplied by seven ( Leviticus 26:14-39, especially verses 18, 21, 23-24, and 27-28). The third concept is that of weeks of years, i.e. years in groups of sevens (Leviticus 25:1-8). There is a fourth idea that is also important in correctly interpreting the seventy weeks. It is the idea that Daniel employs figurative language. Daniel 2:39, for example, uses hyperbole when it says that the third kingdom will rule all over the world. This has never been true of any historical empire. Daniel also uses numbers symbolically. Most Bible scholars feel that the number "seven" is used symbolically in Daniel 3:19; 4:16,23,25, 32, and quite likely in chapter 9 as well. So, while the first three ideas lead nearly all commentators to agree that seventy weeks of years is meant, idea number four tells us that we should not necessarily look for exactness in either the total number of years (490), or in the breakdown into groups of seven weeks (49 years), sixty-two weeks (434 years), and one week (7 years). These are not necessarily exact periods of time any more than the furnace was heated exactly seven times hotter than normal.