## Why I volunteer as a math tutor

Sometimes 8th grade math assignments are unintentionally humorous. Today’s:

Find the volume of each cone. Round the answer to the nearest tenth. (use π = 3.14).

In other words, after telling students to round π to 3 digits of precision, answers with 6 digits of precision were sought. The answer sheet had “Volume =” prompts rather than “Volume ≈” (a wavy “approximately equal” sign, in case it doesn’t render correctly on your browser).

Related:

- Kansas has 10 digits of precision in its child support calculation system (a plaintiff suing someone who earned $1 trillion per month would be able to calculate monthly child support profit of more than $362 million to the nearest dime)

## Tom

December 21, 2016 @ 5:34 am

And isn’t this the sort of question that one normally answers exactly? Or is this more of a piano exercise on the calculator?

If calculators are indeed used anymore. Any thrusting MA parents who have their kids learn Wolfram instead? https://www.wolframalpha.com/pro-for-students/

## Freddie Witherden

December 21, 2016 @ 2:57 pm

The correct prompt should be “Volume ≃” with the symbol being $\simeq$ in LaTeX. Approximately equal to would be valid if some sort of mathematical (as opposed to numerical) approximation was made when deriving the expression for the volume (typically truncating a series). This is not to be confused with “≅” which is generally reserved for “isomorphic to” or “~” denoting similar in magnitude.

Calculator piano exercises are important. One would be amazed how many students not only make mistakes here but also fail to identify obviously bogus numerical answers which are out by orders of magnitudes.

## GrumpyCat

December 22, 2016 @ 1:51 am

I’m not seeing a problem here. Presumably the purpose of the homework is to learn and apply a formula. Significant digits and error bounds is a different lesson.