Exact isn't Always Right

My oldest son is taking Algebra I this year. He had a good question yesterday: "Dad, why does the book only ask us to use 3.14 instead of pi?" I replied with a quizzical look, thinking to myself, "aren't they the same thing?"

He read my thoughts and said, "if I used the calculator, my answer would be more correct, or more precise, right?"

Ahhh...significant digits. That awful, misused concept that makes me think that with more context, my answer is more correct than yours. Or, my son was trying to trick me into using his calculator for math homework. Nice try, son, but no deal.

A = PI(r)^2

So, my area with radius r = 2 is 12.56

His area with radius r = 2 is 12.566370614359172953850573533118, at least according to the Microsoft Windows calculator! Can you set sig digs on this thing?

As we drove away from the soccer field, I tried to explain to him how sometimes the exact answer isn't necessarily the right answer, especially in engineering and manufacturing where just because something was designed a certain way doesn't necessarily mean it can be built that way. Of course, he didn't buy it one bit which has me a bit worried that he will be a (the horror!) a desk engineer or even worse, an industrial engineer! :) I'M JOKING!

So, my next idea to convince him of this concept is to have him build something to a print. Or maybe I'll bring a flashlight home and have him try to assemble it within a theoretical cost accounting generated cycle time limit and then brow beat him for not meeting the cycle time! He might understand then!

Just remember the concept of significant digits when you are breathing down somebody's neck with a stopwatch out in the genba: exact isn't always right!