Why Significant Digits are Important

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Written by William Franz

A story about significant digits, and why their proper usage is important.

 

A machinist is assembling several widgets for a client and realizes that he is out of half-inch bolts.  He tells his new receptionist to fill out an order for 100 bolts and get a quote from ACME-Bolt Company to see how much it will cost.  A half-inch bolt is 0.5 inches, he reminds her.

She sends out an order by FAX which asks for a quote for 100 bolts with the dimensions of 0.50000 inches.  The quote comes back and says that the cost is $8,850,000.

0.5 inch bolts – tolerance 0.05 (5/100) inch, Cast from ordinary iron.  In stock, cost $0.07 (7 cents) each.

0.50 inch bolts – Tolerance 0.005 (5/1000) inch.  Cast from ordinary iron, machine-milled to tolerance.  In stock, cost $0.70 (70 cents) each.

0.500 inch bolts – Tolerance 0.0005 (5/10,000) inch, SPECIAL ORDER, extra-hard alloy to reduce imperfections, specially hand-milled and ground to tolerance, $7/each

0.5000 inch bolts – Tolerance 0.00005 (5/100,000) inch, Replace existing casting equipment $75,000, install carbide milling machine $210,000 and laser micrometer to measure tolerance $55,000.  Custom alloy to reduce imperfections $25/each, Cost per bolt $70.00

                Cost $75k + $210k + $55k + $70/each x100

0.50000 inch bolts – Tolerance 0.000005 (5 one-millionths) inch.  Demolish existing bolt factory, $1,000,000, Install custom alloy facility $500,000.  Graphite mold manufacturing facility $375,000.  Three stage milling Facility $2,100,000.  Laser diffraction calibration equipment $175,000.  Gamma-ray radiation imperfection detection device $2,500,000.  Nuclear Regulatory Agency Fees, Impact Study, Permits and Inspections, $1,500,000.  Lead time approx. 2 years.  Construction to begin after permitting.  Capital expenditures, fees and permitting total $8,150,000

                graphite mold for each bolt $3750

                Custom alloy for each bolt $25

                Labor for bolt (inspection, tolerance testing) $1500

                Cost of bolts approximately $7000 x 100 = $700,0000

                Total cost $8,150,000+ $700,000 = $8,850,000 (Delivery time = 3 years)

 Plus Shipping

 

(This story is of course completely made up.  I remembered hearing something similar as an engineering student perhaps 40 years ago, so I can't credit the original source.  Of course most bolts aren't really cast from iron, but in a story, anything can happen.  When you hear someone looking who is at their calculator say something like 0.5 and 0.50000 are the same thing, you can now explain why they are not).

Sources of Error

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Written by William Franz

I just created a short article titled, "Sources of Error" for students to read and annotate.  This is because students often confound mistakes with sources of error, thinking that both are bad.  Sources of error are present in any laboratory activity, and understanding them demonstrates that you understand how variables affect the outcome of your experiment.  Sources of error should always be discussed in a lab writeup or lab summary.  You can see it here.

Stoichiometry on Teachers-Pay-Teachers

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Written by William Franz

I finally got one of my canvas and moodle files posted for sale on Teachers-Pay-Teachers.

I've been meaning to do it for 2 years, ever since I started writing those monsterously sized question banks.  I just never got around to cleaning them up good enough for showing to the public.

I took 12 quesion banks for Stoichiometry (moles-to-grams, grams- to-moles, and grams-to-grams) and put them in both Moodle and Canvas.  They look the same in both.  I even put examples into my moodlecloud demo site, https://Franz.moodlecloud.com, with a "demouser" login so that people can check them out.

What I haven't done is clean up my amazing Drag-and-Drop virtual card sort for stoichiometry and for dimensional analysis.  It really annoys me that something so useful would be part of the core functionality in Moodle, but isn't even being considered yet in Canvas.

Oh, well....

I need to get onto some of those other question banks I've been meaning to list.  With all the downtime because of this coronavirus thing, I could have gotten a lot done.  Instead I blew it - wasted almost 3-weeks!  Now spending my time writing online curriculum so that we can do distance learning in my shool district.  So much potential....just.....lost.  Next time.

 

Drag & Drop Problems

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Written by William Franz

I've been developing in Canvas for a couple of years now, resorting to good-old php and html sites when I need something Canvas can't do.  After spending a extraordinary amount of time trying to learn more HTML5 so that I could create drag-and-drop question type, I found that there are three versions of that question type now a part of the Moodle core.  I experimented around, found that I could make exactly what I wanted, created it, and published it as an LTI tool.  Then it turns out that Canvas needs to connect to Moodle through SSL.  I buy a certificate, and then find out that of all of Moodle's question types, the Drag-and-drop does not work as an LTI.

What the heck.  Is there no way to get a drag-and-drop question in Canvas??

Here's why this is important.  A drag-and-drop question can be used as a learning tool.  I am trying to teach stoichiometry, and I really want to do a card sort to teach the dimensional analysis.  I could lay out a grid (some people call them train tracks) on a desk, and then have cards with numbers and units for the Given, Molar Masses, Mole Ratio, etc.

Then it hits me - drag and drop is exactly what I'm doing with a placemat-sized grid an a zillion note cards.

If only Canvas would support Drag and Drop question types, or Moodle's LTI worked well with Canvas.  I'll take either.