Put this in your binder. Write your answers on a separate piece of paper.

## Homework: Are Significant Figures Important? A Fable

A student once needed a cube of metal which had to have a mass of 83 grams. He knew the density of this metal was 8.67 g/cm3, which told him the cube’s volume. Believing significant figures were invented just to make life difficult for chemistry students and had no practical use in the real world, he calculated the volume of the cube as 9.573 cm3. He thus determined that the edge of the cube had to be 2.123 cm. He took his plans to the machine shop where his friend had the same type of work done the previous year. The shop foreman said, “Yes, we can make this according to your specifications—but it will be expensive.”

“That's OK,” replied the student. “It’s important.” He knew his friend has paid \$35, and he had been given \$50 out of the school’s research budget to get the job done.

He returned the next day, expecting the job to be done. “Sorry,” said the foreman. “We're still working on it. Try next week.” Finally the day came, and our friend got his cube. It looked very, very smooth and shiny and beautiful in its velvet case. Seeing it, our hero had a premonition of disaster and became a bit nervous. But he summoned up enough courage to ask for the bill. “\$500, and cheap at the price. We had a terrific job getting it right—had to make three before we got one right.”

“But…but…my friend paid only \$35 for the same thing!”

“No. He wanted a cube 2.1 cm on an edge, and your specifications called for 2.123 cm. We had yours roughed out to 2.2 cm that very afternoon, but it was the precision grinding and lapping to get it down to 2.123 cm which took so long and cost the big money. The first one we made was 2.103 cm on one edge when we got finshed, so we had to scrap it. The second was closer, but still not what you specified. That’s why the three tries.”

“Oh!”

Answer the following questions on a separate piece of paper using complete sentences where appropriate and showing all mathematical work where appropriate.
1. Density is defined as D = mass ÷ volume. In this story, the density of the metal is 8.67 g/cm3. Solve the equation (D = m/V) for V and find the volume of a cube if the mass of the cube is specified to be 51 g.
2. The volume of a cube is V = s3. Now that you have the volume, find the length of the side of the cube.
3. What did the student in the story do wrong?
4. Why did the mistake cost so much?
5. So how should you report the value of the length of a side of the cube?
Note: Be prepared to discuss this story in class!

This text originally found at http://www.chemteam.info/SigFigs/SigFigsFable.html
Last updated: Oct 25, 2006 Home