What causes "Non-terminating decimal expansion" exception from BigDecimal.divide?

Here's the problem

bd1.divide(bd2)

You need to use one of the overloaded divide() methods that takes a rounding mode (in various forms) - you cannot do the rounding after the division because with a nonterminating fraction the intermediate result would either already need to be rounded, or require infinite storage space.

The problem is caused by an operation (division) that would result in a recurring decimal.

The solution is to specify a scale when performing a division, for example:

BigDecimal one = new BigDecimal("1");
BigDecimal three = new BigDecimal("3");
BigDecimal oneDivThree = one.divide(three, 200, RoundingMode.HALF_UP);

Non-terminating decimal need rounding

When using divide you should use a MathContext with RoundingMode in case the exact result has an infinite number of decimals.

Such is your case:

MathContext mc = new MathContext(2, RoundingMode.HALF_UP) ;
BigDecimal bd3 = bd1.divide(bd2, mc);

Alternatively call divide with a rounding mode to use the scale of the numerator (bd1 in the example below):

BigDecimal bd3 = bd1.divide(bd2, RoundingMode.HALF_UP);