Mr. Challenge Math

I will be posting a math lesson every week for the next few months. Here is number one:

The incorrect placement of decimals points can be fatal!

A roadside fruit stand near Seattle, Washington, had a sign advertising a low price for apples:

Apples: Only .50 cents each!!

A customer picked out 15 apples, brought them to the counter, handed the clerk a dime and said “keep the change.” The clerk looked confused and said a dime was not enough money to buy 15 apples. He said that the cost for 15 apples would be $7.50. The customer pointed to the sign and insisted that a dime was more than enough to pay for 15 apples. “Your sign clearly states that apples are .50 cents, or a half cent each. Fifteen apples at half a cent each would be 7.5 cents. I am being generous and letting you keep the extra two and a half cents!”

Stores are not the only places that make mistakes with decimal points. Arizona voters passed a ballot initiative that was supposed to have raised the tax on ci******es by 80 cents per pack. The to***co companies fought this tax increase, but were pleasantly surprised when they saw that the ballot language called for an increase of .80 cents per pack. Unfortunately, the people writing the ballot didn’t have a math teacher check the wording before it went to print. Just as in the story about the fruit stand where the clerk thought that .50 cents was the same as .50 dollars, the people who wrote the language for the ballot initiative in Arizona thought that .80 cents was the same as 80 cents. After losing the ballot initiative, the to***co companies were not upset because the ballot language meant the extra tax would only be 8/10 of a cent per pack sold instead of 80 cents.

The misplaced decimal at the fruit stand did not have serious consequences, but the misplaced decimal point that occurred in the Arizona election caused an enormous headache for the state and cost a significant amount of money to correct. Misplaced decimal points can not only cost money, but in some cases they can even be life threatening.

A researcher at Northumbria University (England) decided to conduct a study about the effects of caffeine on exercise. Two students volunteered to take part in the study, but quickly regretted their decision. The experiment called for each participant to receive a dose of .3 grams of caffeine, but because of a misplaced decimal point, they were each given 30 grams of caffeine. Shortly after ingesting the caffeine, both men started vomiting, shaking, and their heartbeats rose to dangerous levels. After being hospitalized, the hospital toxicologist said they could have both easily died from the caffeine overdose.

The researcher intended to give each volunteer a dose of .3 grams of caffeine, which is the equivalent of about three cups of coffee. The 30 grams each participant was given was the equivalent of instantaneously drinking 300 cups of coffee! The two students were actually very lucky because 18 grams of caffeine is considered a fatal dose.

So what ended up happening in these three cases of misplaced decimal points?

Fruit stand: The customer agreed to pay the $7.50 price for 15 apples with the understanding that the clerk would change the sign to read: Apples: 50 cents each.

Arizona ballot mistake: The courts eventually decided to allow the state to collect an 80 cent per pack tax on ci******es because all information leading up to the election talked about 80 cents and not .80 cents.

Caffeine experiment: The two students eventually recovered. After an inquiry, Northumbria University was required to pay a fine of $500,000 for its life-threatening decimal point placement error.

Math thought for the day:

There are more zeros in the number googolplex than there are atoms in the entire universe.