I used DecimalFormat for formatting the BigDecimal instead of formatting the String, seems no problems with it.

The code is something like this:

bd = bd.setScale(2, BigDecimal.ROUND_DOWN);

DecimalFormat df = new DecimalFormat();
            
df.setMaximumFractionDigits(2);
            
df.setMinimumFractionDigits(0);
            
df.setGroupingUsed(false);

String result = df.format(bd);

To get exactly 10.0001 you need to use the String constructor or valueOf (which constructs a BigDecimal based on the canonical representation of the double):

BigDecimal bd = new BigDecimal("10.0001");
System.out.println(bd.toString()); // prints 10.0001
//or alternatively
BigDecimal bd = BigDecimal.valueOf(10.0001);
System.out.println(bd.toString()); // prints 10.0001

The problem with new BigDecimal(10.0001) is that the argument is a double and it happens that doubles can't represent 10.0001 exactly. So 10.0001 is "transformed" to the closest possible double, which is 10.000099999999999766941982670687139034271240234375 and that's what your BigDecimal shows.

For that reason, it rarely makes sense to use the double constructor.

You can read more about it here, Moving decimal places over in a double

BigDecimal is immutable, any operation on it including setScale(2, BigDecimal.ROUND_HALF_UP) produces a new BigDecimal. Correct code should be:

BigDecimal bd = new BigDecimal(1);
bd.setScale(2, BigDecimal.ROUND_HALF_UP); // this does NOT change bd
bd = bd.setScale(2, BigDecimal.ROUND_HALF_UP);
System.out.println(bd);

Output:

1.00

Note:

Since Java 9 BigDecimal.ROUND_HALF_UP has been deprecated and you should now use RoundingMode.HALF_UP.