java.lang.ArithmeticException: Non-terminating decimal expansion; no exact representable decimal result

Problem
As I execute the following code snippet

   public static void main(String args[]) {  
     BigDecimal one = new BigDecimal(1);  
     BigDecimal two = new BigDecimal(2);  
     BigDecimal three = new BigDecimal(3);  
     System.out.println(one.divide(two));  
     System.out.println(one.divide(three));  
   }  

The console showed:

0.5  
 Exception in thread "main" java.lang.ArithmeticException: Non-terminating decimal expansion; no exact representable decimal result.  
      at java.math.BigDecimal.divide(BigDecimal.java:1616)  
      at gov.nta.fms.web.rest.Fms421rResource.main(Fms421rResource.java:204)  

Why one.divide(two) is working fine?  But failed to execute one.divide(three) ?

Root Cause
Because I am not specifying a precision and a rounding-mode. 
BigDecimal is complaining that it could use 10, 20, 5000, or infinity decimal places, so it cannot be able to show me the exact representation of the number.

We need to assign its scale and rounding mode, please check the following code snippets:

   public static void main(String args[]) {  
     BigDecimal one = new BigDecimal(1);  
     BigDecimal two = new BigDecimal(2);  
     BigDecimal three = new BigDecimal(3);  
     System.out.println(one.divide(two));  
     System.out.println(one.divide(three, 2, BigDecimal.ROUND_HALF_UP));  
   }  

Here is java doc:

• divide

  public BigDecimal divide(BigDecimal divisor,
                  int scale,
                  int roundingMode)

  Returns a BigDecimal whose value is (this / divisor), and whose scale is as specified. If rounding must be performed to generate a result with the specified scale, the specified rounding mode is applied.The new divide(BigDecimal, int, RoundingMode) method should be used in preference to this legacy method.

  Parameters:

  divisor - value by which this BigDecimal is to be divided.

  scale - scale of the BigDecimal quotient to be returned.

  roundingMode - rounding mode to apply.

  Returns:

  this / divisor

  Throws:

  ArithmeticException - if divisor is zero, roundingMode==ROUND_UNNECESSARY and the specified scale is insufficient to represent the result of the division exactly.

  IllegalArgumentException - if roundingMode does not represent a valid rounding mode.

  See Also:

  ROUND_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR, ROUND_HALF_UP, ROUND_HALF_DOWN, ROUND_HALF_EVEN, ROUND_UNNECESSARY

The console showed:

 0.5  
 0.33  

Reference
[1] http://docs.oracle.com/javase/7/docs/api/java/math/BigDecimal.html#divide(java.math.BigDecimal,%20int,%20int)