Unique Scaling?

So I'm following a programmer who has done a few things that I don't completely understand. This is in a GE RX3i PLC. First of all, he used 250 ohm resistors for analog inputs, effectively making everything 1 to 5 Volts. In a GE PLC, that corresponds to 3200 to 16000 counts.

To convert to engineering units, rather than use floating point and y=mx+b, the previous programming did something I've never seen before. He combined a divide, subtract, multiply, and divide block. For instance, to convert 3200-16000 to 0-600: y=(x/8 - 400)(3/8). It looks like the point of this is to avoid an overflow when multiplying the x times the slope. A 3/8 has been factored out of what would be the normal y=mx+b equation.

My question is: is this commonly done?

My second question is: what about when you're going to something that's not a nice, even range. Like 0 to 1875 or something like that. How do you go about coming up with the equation in the form that I mentioned above?

Thanks.

Scaling formula

(((Scaled Max-Scaled Min)/(Max Raw Input-Min Raw Input))*(Raw Input-Min Raw Input))+Scaled Min = Scaled Value

The 250 ohm resistors are probably to convert a 4-20mA signal into voltage for analog inputs that don't directly accept current inputs.

Ok, I appreciate the help, but I was specifically asking about the formula that was used in the original post. Is that unusual? How does one go about calculating the constants for that form of the equation?

The original formula has the transmitter range of 0-600 factored into it, presumably to make the numbers smaller and the formula simpler for the original programmer.

No, this isn't common.

The form Mickey provided is more common. I prefer it because you can use registers containing the transmitter full scale and min values in the formula, and then if the transmitter changes you can easily change the register values without messing up your program.