Mathematics Education

You will notice that this article on the new http://finance.yahoo.com/news/meet-100-bill-world-most-154245088.html] $100 banknote says there are 820 million Benjamins in circulation. A large portion of hundreds are held outside the United States.

They link to a site that says as of June 30, 2012 there is $820 billion dollars in c-notes circulating. So clearly $820 billion divided by $100 is 820 million.

What is equally disturbing besides the ability to do simple math, and run the mistake by all the editors, is that nobody thinks that is an incredibly small amount of value for the world's most popular currency. Just on common sense alone, you would think someone would catch the mistake.

Quote: Pacomartin

You will notice that this article on the new http://finance.yahoo.com/news/meet-100-bill-world-most-154245088.html] $100 banknote says there are 820 million Benjamins in circulation. A large portion of hundreds are held outside the United States.

They link to a site that says as of June 30, 2012 there is $820 billion dollars in c-notes circulating. So clearly $820 billion divided by $100 is 820 million.

What is equally disturbing besides the ability to do simple math, and run the mistake by all the editors, is that nobody thinks that is an incredibly small amount of value for the world's most popular currency. Just on common sense alone, you would think someone would catch the mistake.

I feel you on the sadness of the basic math error.

However, on the second part, I have to disagree that a common person would notice it. Honestly I don't think many people pay attention to it or have any idea how much physical currency is out there circulating. Even with you posting about it all the time, if I heard a figure that was off by a factor of ten or even 100, I probably wouldn't give it any mind.

EDIT: Looking at your post again, don't you mean the correct figure is 8.2 billion?

Quote: AcesAndEights

EDIT: Looking at your post again, don't you mean the correct figure is 8.2 billion?

Yes, of course it is 8.2 billion. I was trying to be sarcastic (not successfully).

The writer wrote
There were more than 820 million Ben Franklins out in the world at the end of last year, making it the most popular bank note, by value, among the world’s major currencies. and he hot linked 820 million Ben Franklins to a website that says there are $820,155,828,300 dollars in $100 notes in circulation as of June 30, 2012.

My principal comment is if you are looking at something that says about $800 billion in $100 notes, you should realize that is roughly 8 billion notes. That is pretty low level mathematics for someone who writes a finance column.

My secondary comment is 820 million banknotes for a population of 315 million should hit most people as way too small of a number. That is less than 3 per person. Mind you this same author notes that most c-notes are circulating overseas. Even if you didn't know the exact number, you should realize that it is more then 3 per person. There are more $2 banknotes than 820 million, and you never see those circulating.

An educated person should know "orders of magnitude". If I ask you what the circumference of the Earth is in kilometers, and you hear the answer 40 million kilometers, an educated person should recognize that answer as impossibly large. A reasonably educated person should be able to tell you that the correct answer is 40 thousand kilometers because that is basically the definition of a kilometer. It is a 1000 meters, and meters were defined in the 18th century as exactly the distance that would make 40 million meters equal to the circumference of the earth.

If you look it up it says the circumference is 40,008 kilometers through the poles and 40,075 kilometers at the equator. But that is a modern calculation which is slightly more accurate than what they could do in the 18th century (the original definition was through the poles).

Some people just gloss over the math particularly at the million/billion/trillion levels where it is really beyond comprehension anyway.

Sure there are times when its important... such as some ordnance that changed a tax rate by ten mils instead of ten percent or something. And programs that control complex processes have to be more accurate, but people tend to "turn off" at certain points.

If it were one dollar bills perhaps the editors would have been alert. I don't know. I imagine most readers never caught the error at all.
And were none the worse for wear over it.

Quote: Fleastiff

Some people just gloss over the math particularly at the million/billion/trillion levels where it is really beyond comprehension anyway.

There are over 3000 comments on that article, and while hundreds are about putting President Obama's face on the new bill and it seems like everyone thinks they are hysterical by commenting that the $100 bill is worth $50, $40, $10, or $1 not one person noticed the number is way to low to make sense. Many people said they forgot what the old ones look like.

The quantityt $80 billion would make sense in the President Carter era, but we are in a world of trillion dollar deficits. Quantities like $80 billion are chump change today in global finance.

North Korea says US owes them $75 trillion in a lawsuit

How much does North Korea owe for its top notch counterfeiting of various currencies?

Consider: At times a DNA technician may have to testify regarding numbers that are beyond the total number of people in the world. Are such numbers really within the comprehension of the average juror?

Dilbert's famed sale of discounted lottery tickets with one fifty-millionth less of a chance to win makes us wonder how people judge numbers. The chance of winning without having a ticket is zero but the chance of buying a lottery ticket and then winning is so very close to zero as well. The difference is purely emotional, not quantitative.

I'm a person whose eyes glaze over when the math gets challenging but I do realize that others have more staying power and might catch an order of magnitude error. I merely glance at the figures and suspect one. Is my math deficient in this instance?

During the Falklands 'War' the British flew the soon to be retired Vulcan bombers 8,000 miles and used a cheapie pocket calculator for navigational purposes to bomb a critical runway. Does such lack of scientific instrumentation invalidate the event or intensify its success? Is using a bicycle chain in an on-board analog bombing computer an insult to mathematics? Eleven Vulcan tankers had to fly that mission just to get that one Vulcan bomber there. Yet cheapie calculators available from street vendors were used.

Quote: Fleastiff

I'm a person whose eyes glaze over when the math gets challenging but I do realize that others have more staying power and might catch an order of magnitude error. I merely glance at the figures and suspect one. Is my math deficient in this instance?

In my job we used to get involved in a lot of public hearings, and I was amazed at how impervious people were to order of magnitude errors. They simply believe anything that someone tells them.

A standard width of a time zone at 25 degrees is 940 miles, and at 45 degrees is 732 miles. If I ask you how wide is a time zone, and you say a thousand miles, at least you are in the order of magnitude, if you say 10,000 miles or 100 miles then I have to wonder about your comprehension of the world.

Quote: Pacomartin

Yes, of course it is 8.2 billion. I was trying to be sarcastic (not successfully).

Sorry, I don't pick up on that stuff very well (in person, let alone on the web).

Quote: Pacomartin

My secondary comment is 820 million banknotes for a population of 315 million should hit most people as way too small of a number. That is less than 3 per person. Mind you this same author notes that most c-notes are circulating overseas. Even if you didn't know the exact number, you should realize that it is more then 3 per person. There are more $2 banknotes than 820 million, and you never see those circulating.

An educated person should know "orders of magnitude". If I ask you what the circumference of the Earth is in kilometers, and you hear the answer 40 million kilometers, an educated person should recognize that answer as impossibly large. A reasonably educated person should be able to tell you that the correct answer is 40 thousand kilometers because that is basically the definition of a kilometer. It is a 1000 meters, and meters were defined in the 18th century as exactly the distance that would make 40 million meters equal to the circumference of the earth.

If you look it up it says the circumference is 40,008 kilometers through the poles and 40,075 kilometers at the equator. But that is a modern calculation which is slightly more accurate than what they could do in the 18th century (the original definition was through the poles).

I think you're giving the vast majority of Americans too much credit in the intelligence department.

Quote: AcesAndEights

I think you're giving the vast majority of Americans too much credit in the intelligence department.

I had this problem at work as well. We had two bidders bid $75 million to do a contract that used to be $150 million. I said at the time that is an order of magnitude change and requires a breakthrough in technology. You can't do that kind of improvement by improving bookkeeping, small improvements in manufacturing, reduction of management, etc. We are getting thousands of pages of bullcrap.

Of course, everyone received their huge bonuses for saving the government so much money, and the contractor defaulted in 90 days.

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Same thing with the proposed high speed train to the new airport in the desert in San Diego. There is only one high speed train (200+ mph) from the city center to the airport in the entire world and that is in Shanghai, London, Rome, Tokyo, Oslo all have "really fast" 60-120 mph trains that go to their city centers and Paris has a train station where you can catch a high speed rail to other parts of the country. Keep in mind that Tokyo doesn't have a high speed rail to city center and they are the most intense train travelers on the planet.

The builders of the high speed train in Shanghai literally posted a press release that the train is the most expensive advertising project in history. They were hoping to build a train from Beijing to Shanghai, and so the German government subsidized what would be an insane proposition from a business prospective. Nobody needs to go up to 268 mph on a 19 mile trip.

You can never ever build a high speed train to the airport in San Diego. It is a massive "order of magnitude" change in business sense and in behavior. Yet the idea persisted for years, and bought multiple trips to Shanghai for city executives.

Most people don't know what "orders of magnitude" even means. Why don't you say "You're wrong by a factor of one hundred million", for example? That sinks in pretty fast.

Most people are also clueless about percentages. Here, last month I had an argument with a coworker who insited if you remove 4% from X, then add 4% to the result, you have to get back exactly to X. Of course if Y=X-4% then Y+4%<>X because if Y=100-4% then Y=96 and 96+4%=99.84 and 99.84 does not equal 100.