Details

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).

Details

Written by William Franz

• chemistry
• Charles' law
• Boyle's law
• Gay-Lussac's law
• avogadro's law
• practice

There is currently a new page that supports an unlimited number of practice problems for four common gas laws:  Boyle's Law, Charles' Law of Volumes, the Gay-Lussac Law (which is more commonly known as Amontons' Law of Pressure-Temperature) and Avogadro's Law.  An entire website here at FranzScience is dedicated to lessons and practice in science, particularly chemistry.  The website is http://practice.franzscience.com, and it currently has the laws mentioned above as well as unlimited practice in two stoichiometry categories.

More laws are planned.  First will be the Combined Gas Law, Dalton's law of partial pressures, and finally the Ideal Gas Law, PV=nRT.  All of the laws in the gas law section have both a brief description of the law (and who it is named after, if applicable) and examples of its use, and most notably a page that allows students to try an unlimited number of automatically graded practice problems.

In the stoichiometry section there are 70 different balanced equations.  The numbers for grams-to-grams calculations and limiting reactant calculations are generated randomly, so there are virtually an unlimited number of combinations.

In the gas law sections, the individual laws available so far only support one set of units.  Pressure is in atmospheres, volume in liters, and temperature in Kelvin.  Future versions will support multiple units and require the student to occasionally convert, as would occur in real problems on worksheets, quizzes or exams.

Stay tuned to see as new laws are added.  After this unit is over, we will move on to Unit 12 - Solutions and Solubility.