 Solution

Round-off error arises from representing numbers and carrying out arithmetic at finite precision: storing $1/3$ or subtracting nearly equal numbers can lose information even when the mathematical algorithm is exact. Truncation error arises from replacing a continuous or infinite mathematical operation by a finite approximation, such as discarding higher Taylor series terms in a finite difference. Refining a grid usually reduces truncation error but may increase accumulated round-off error; the two have different origins.