Using floor, ceiling, and standard arithmetic notation, give an expression for a real number x . . . 1 . . . rounded to the nearest integer. (“Round up” for a number that’s exactly between two...

Using floor, ceiling, and standard arithmetic notation, give an expression for a real number x . . .

1 . . . rounded to the nearest integer. (“Round up” for a number that’s exactly between two integers—for example, 7.5 rounds to 8.)

2. . . . rounded to the nearest 0.1.

3. . . . rounded to the nearest 10−k, for an arbitrary number k of digits after the decimal point.

4. . . . truncated to k digits after the decimal point—that is, leaving off the (k + 1)st digit and beyond

(For example, 3.1415926 truncated with 3 digits is 3.141, and truncated with 4 digits is 3.1415.)