This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
The reason for the difference between 2.34 and 2.33 is that when you say a.divide(b,2)), that "2" is the rounding mode - which is BigDecimal.ROUND_CEILING. While "3" is BigDecimal.ROUND_FLOOR. In one case you're telling the computer to round up, and in the other you're telling it to round down. No surprise there. If you want it to round to whichever is closest, use BigDecimal.ROUND_HALF_DOWN or BigDecimal.ROUND_HALF_UP. The difference is very minor. You can examine the JavaDoc to learn the exact differences between rounding modes.
If you're asking why the result is 2.33 rather than 2.33333 or 2.3333333333333 or 2.333333333333333333333333333333333 or whatever, then the answer is that you need to tell it how many digits you want. If you want 10 digits after the decimal point, use a scale of 10:
If you want more digits or less, use another number besides 10.
Since you originally did not specify the number of digits you wanted, BigDecimal assumed you wanted the same number as were used for the first BigDecimal in the calculation, a. Since you created this as 14.00, it had two digits after the decimal. That's what was used in your original answers, 2.34 and 2.33.