Science Puzzle
The 68,000,003-Year-Old Dinosaur
A visitor asks a museum guard how old the Tyrannosaurus rex skeleton is. "Sixty-eight million and three years," says the guard proudly. "When I started working here three years ago, the expert told me it was 68 million years old."
What's wrong with the guard's answer?
The Answer
The guard's sum is right but meaningless. The original 68 million was never accurate to the nearest year, so adding three years to it gives an answer that sounds precise but isn't.
Fossils like this are usually dated by measuring radioactive elements in layers of volcanic ash above and below the bones. Those elements decay at a known, steady rate, which gives an age, but always with an uncertainty, often tens or hundreds of thousands of years either way. "68 million" really means "somewhere close to 68 million, give or take a fair bit". The three years the guard added are far smaller than that uncertainty, like adding a grain of sand to a guess at the weight of a beach.
Scientists show how precise a number is by how many digits they give, known as significant figures, or by stating the uncertainty directly. Writing 68,000,003 suggests the age is known to the year; writing 68 million says it's known only roughly.
The same trap turns up everywhere: a survey of a few hundred people reported as 37.42%, or a calculation done with rough estimates and then given to six decimal places. A result can't be more precise than the rough numbers it was made from.
The principle: Precision and significant figures. A result is only as precise as its least precise ingredient; extra digits beyond the uncertainty add false confidence, not knowledge.