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.
She thinks this is a bit strange, so she asks why they are so expensive, and if the have any cheaper half-inch bolts.
This is the information on the fax that came back
0.5 inch bolts – tolerance 0.05 (5/100) inch, Cast from ordinary iron. In stock, cost $0.07 (7 cents) each.
Total cost $7.00 (Delivery time = same day)
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.
Total cost $70.00 (Delivery time = same day)
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
Total cost $700.00 (Delivery time = 2 weeks)
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
Total cost $347,000 (Delivery time = 3 months)
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)
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(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).
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