Learn to Program with Small Basic

Round()
-4 -3.5 -3 0 3 3.5 4
Round() behaves mostly how you’d expect it to
when rounding a number. Above 0.5, it’ll round
up; below 0.5, it’ll round down.
Floor()
-4 -3.5 -3 0 3 3.5 4
Floor() always rounds down, throwing away
any partial fraction of a whole. Look at what
happens with negative values!
Ceiling()
-4 -3.5 -3 0 3 3.5 4
Ceiling() always rounds up.
Math.Round(3.4) = 3
Math.Round(3.6) = 4
Math.Round(-3.4) = -3
Math.Round(-3.6) = -4
Math.Floor(3.4) = 3
Math.Floor(3.6) = 3
Math.Floor(-3.4) = -4
Math.Floor(-3.6) = -4
Math.Ceiling(3.4) = 4
Math.Ceiling(3.6) = 4
Math.Ceiling(-3.4) = -3
Math.Ceiling(-3.6) = -3
Figure 7-1: The rounding methods with example arguments and return values
Traditional Rounding
Be careful when you use the Round() method if the fraction part of the number
is exactly 0.5. In this case, the Round() method rounds to the nearest
even integer (this is called banker’s rounding). For example, 0.5 and –0.5 are
rounded to 0, 1.5 and 2.5 are rounded to 2.0, and –1.5 and –2.5 are rounded
to –2. This is different from what you learned in algebra, where the 0.5 fractions
always round up to 1! Even though it’s not what you’re used to, banker’s
rounding is very common and is regularly used by bankers, which gives it
its name.
But how can we make Small Basic round numbers the way you learned
in school (where the 0.5 fraction is always rounded up)? We’ll do some fancy
footwork using the Floor() method instead of the Round() method, like this:
Math.Floor(x + 0.5)
Using this trick, x represents whatever value you want to round. So if x
is 0.6, then x + 0.5 = 1.1, and Floor(1.1) = 1. Cool! That’s exactly how we’d
expect it to work.
But let’s say x is 2.5. If we just used Math.Round(2.5), we would get 2, which
isn’t the result you would want if you wanted to use traditional rounding.
We want to round up and get 3. Using our fancy trick, you’d get x + 0.5 =
3.0, and Floor(3.0) = 3. Now that’s more like it! This gets the values you’d
expect if you wanted to round a number with a .5 fraction.
Empowering Programs with Math 87