# A "Sig Figs" Story

Author Unknown

A student once was given the assignment to make a cube of a metal with a mass of 83 grams. He knew the density of the metal was 8.67 g/cm^{3}. Using his calculator, he found that the required volume would be 9.573 cm^{3}. Taking the cube root of the volume gave him the length of each edge of the cube, 2.1233 cm. He drew up plans for the cube and took them to a local machine shop that his friend had used to do the same job a year earlier.
The foreman said "Yes, we can make this according to your specifications, but it will be expensive."

"That's okay," replied the student. "It's important."

He knew that his friend had paid $35.00 and he himself had been given a budget of $50.00 to get the job done.

He returned the next day, expecting to pick up the cube. "Sorry," said the foreman. "We're still working on it. Try next week."

Finally the day came, and our student got his cube. It looked very smooth and shiny and beautiful in its velvet lined case. Seeing it, our hero had a premonition of disaster and became a bit nervous, but he gathered up enough courage to ask for the bill. "$525.00 and cheap at the price. We had a terrible time getting it right... had to make three before we finally got it."

"But -- but -- my friend paid only $35.00 for the same thing!"

"No. He wanted a cube 2.1 cm on an edge, and your specification called for 2.1233 cm. We had yours roughed out to 2.1 cm that afternoon, but it was the precision grinding and lapping to get it down to 2.1233 cm which took so long and cost the big money. The first one we made was 2.0895 cm on one edge when we finished, so we had to throw it away. The second one was closer, but still not what you specified. That's why the three tries."

"Oh."

**MORAL:** Calculators can increase speed, but never precision.