First day of class. Not ready to retire quite yet. Wearing my new plaid shirt. In today’ Globe there’s an article on organic food purchase – $31.4 billion is 4.2% of the annual US retail total, I think I will start by asking the class to estimate total retail food sales and then check the numbers from the paper.
The class is half freshmen (and women) who don’t know where they are going and want to get their math out of the way, half seniors who waited until the last minute to meet the qr requirement. Maybe I’ll pair them up today in teams of two.
Good class – at least I thought so. I asked for total annual retail food sales in the US and had them work in groups of 2 or 3. Got a range of answers from $1 billion to $1,000 billion, so could talk about getting the number of zeros right. When I asked for methodologies several people volunteered that they just guessed – which led to good laughs.
We finally settled on this estimate. Start with 300 million people (a number they’ll now remember). Figure between 2 and 4 people per household – and use 3 because it makes the arithmetic easier. That means 100 million households. We agreed that $100 to $400 dollars per week per household sounded right, so nationwide between $10000 million and $40000 million per week – or, moving to billions, between $10 and $40 billion per week. By this time they were genuinely happy to use 50 weeks per year rather than 52, to come up with a final answer of between $500 billion and $2,000 billion = $2 trillion.
So far so good. Then I dug out the newspaper and gave them the $31.4 billion and 4.2% figures. The room fell silent. Percentages – OMG! Too bad – we pushed on through the calculation:
$31.4 billion / 0.042 = $747.619… billion
In curly arithmetic (using ~ instead of =), which they enjoyed, that’s just about $750 billion. All we’re entitled to are two significant digits since that’s all we have in the 4.2%. And it’s right in our back-of-an-envelope Fermi problem estimate.
We then searched the web for the answer, and came up with a similar number from the census bureau web page (sparking a good discussion about whether using the web was OK in this class – yes – and whether it was reliable – sometimes, and you have to think about it.
The students were impressed (surprised) that all three methods led to the same answer – and that one of them required very little more than common sense and counting zeroes.
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