Math weirdness: Infinite gold is not enough

A man has a 10 lb gold bar and wants to divide it equally among his three children. He gets his wife’s cooking scale out and perfectly divides the bar into 3 equal pieces and gives one to each of his kids.

One of his kids is a scientist who works for NASA. This kid wants to make sure he got an equal share, so he takes his piece of gold to the world’s most sensitive scale.

The kid places his bar on the scale and gets an initial reading: 3.33lbs. Looks like dad measured right. The kid turns the dial to get an even more accurate measure: 3.333 lbs. Great! He has more gold than just 3.33 lbs.

He turns the dial again: 3.3333lbs. Nice! Even more than 3.333! The kid keeps turning up the sensitivity and keeps realizing his piece of gold is heavier than what the last reading showed. Surely at some point its weight will max out and the next number will be 0, right? If its mass is not changing, how can we not get an exact measure? It never happens.

The kid is freaked out and wants to return the gold. He convinces his two siblings to melt and recombine their gold into one bar to give back to their dad.

The dad, wanting to make sure he got back all 10 lbs, takes the bar to his scientist kid’s lab and places it on the scale and turns the sensitivity all the way up: 9.99999999999999999999 lbs. Those sons of bitches.