Difference between valueOf() and String.format()

Question

Why are the values of String.valueOf(5.6d + 5.8d) and String.format("%f", 5.6d + 5.8d) diffrent?

String.valueOf(5.6d + 5.8d) will print "11.399999999999999".
String.format("%f", 5.6d + 5.8d) will print "11.400000".

Why is it so?

Edit: The question differs to Is floating point math broken? , because String.format() round up (see answers)

Answer 1

From the documentation of Format Strings for String#format:

If the precision is less than the number of digits which would appear after the decimal point in the string returned by Float.toString(float) or Double.toString(double) respectively, then the value will be rounded using the round half up algorithm.

By default, String.format("%f", ...) uses 6 decimal digits of precision; because this is fewer digits than what would appear when used by Double.toString(double) (which is equivalent to String.valueOf(double)), then the value is rounded as specified above.