Rounding

Rounding down

round down (or take the floor, or round towards minus infinity): q is the largest integer that does not exceed y.

Rounding up

round up (or take the ceiling, or round towards plus infinity): q is the smallest integer that is not less than y.

Rounding towards zero

round towards zero (or truncate, or round away from infinity): q is the integer part of y, without its fraction digits.

Rounding away from zero

round away from zero (or round towards infinity): if y is an integer, q is y; else q is the integer that is closest to 0 and is such that y is between 0 and q.

Comparison of approaches for rounding to an integer

Value	Directed rounding				Round to nearest
Round down (towards −∞)	Round up (towards +∞)	Round towards zero	Round away from zero	Round half down (towards −∞)	Round half up (towards +∞)	Round half towards zero	Round half away from zero	Round half to even	Round half to odd
+1.6	+1	+2	+1	+2	+2	+2	+2	+2	+2	+2
+1.5					+1	+2	+1	+2	+2	+1
+1.4						+1		+1	+1
+0.6	0	+1	0	+1					+1
+0.5					0		0		0
+0.4						0		0		0
−0.4	−1	0		−1				0		0
−0.5					−1			−1		−1
−0.6						−1	−1		−1
−1.4	−2	−1	−1	−2					−1
−1.5					−2			−2	−2
−1.6					−2	−2	−2	−2	−2	−2

Favorite site

Wikipedia (en) Rounding