For small numbers of at-bats, it is possible (though unlikely) for a player's on-base percentage to be lower than his batting average (H/AB). This happens when a player has almost no walks or times hit by pitch, with a higher number of sacrifice flies (e.g. if a player has 2 hits in 6 at-bats plus a sacrifice fly, his batting average would be .333, but his on-base percentage would be .286). The player who experienced this phenomenon with the most number of at-bats over a full season was Ernie Bowman. In 1963, with over 125 at-bats, Bowman had a batting average of .184 and an on-base percentage of .181
The main application of slugging percentage is to go beyond just being able to tell how good a player is at getting hits, but how good they are at getting quality hits. For example, Robinson Cano and Andrew McCutchen both had a batting average of .314 last year; however Cano slugged just .454 opposed to McCutchen who finished with a .542 mark. While both players got hits just as often, McCutchen got the more valuable kinds of hits more often (he had more doubles, triples, and homers than Cano), so he was the better hitter in 2014.
Every hitter is entitled to their own style or preference when it comes to stance, set-up, and load. However, when the stride foots lands, all hitters are very much alike in their movements to and through contact. My emphasis will focus on the “non-negotiable” of consistent, hard contact—bat path. Learning to control the bat barrel is an enormous step forward in becoming the best hitter they can be.  
If you take a batting average and multiply it by 100 (or slide the decimal point over two spots to the right), it will give you a raw percentage of how often a player gets a hit. So using Mike Trout’s batting average as an example, he accumulated 172 hits in 602 at bats last year for a batting average of .287 (172/602). Multiplying .287 by 100 gives you 28.7 which tells you that in 2014, Mike Trout averaged a hit in 28.7% of his at bats.

Please note that these percentiles apply only to hitters who qualified for the batting title. The requisite OBP for the various percentiles would be lower if all hitters were included, because subpar players tend to not collect enough plate appearances to qualify for the batting title. Stated another way, these figures only reflect the performance of regulars.

Henry Chadwick, an English statistician raised on cricket, was an influential figure in the early history of baseball. In the late 19th century he adapted the concept behind the cricket batting average to devise a similar statistic for baseball. Rather than simply copy cricket's formulation of runs scored divided by outs, he realized that hits divided by at bats would provide a better measure of individual batting ability. This is because while in cricket, scoring runs is almost entirely dependent on one's own batting skill, in baseball it is largely dependent on having other good hitters on one's team. Chadwick noted that hits are independent of teammates' skills, so used this as the basis for the baseball batting average. His reason for using at bats rather than outs is less obvious, but it leads to the intuitive idea of the batting average being a percentage reflecting how often a batter gets on base, whereas in contrary, hits divided by outs is not as simple to interpret in real terms.