Architectural Flashing Supply
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Trade mathematics and unit conversions · Lesson 4 of 4

Trade mathematics and unit conversions: defects, verification and case study

The common math defects in a flashing take-off, how computers round, a constructed L-shaped coping take-off with four planted errors and their corrections, the estimate-and-reverse check, the record to keep, and the limits of calculator results.

You will be able to: Diagnose plan-length, rounded-factor, early-rounding, wrong-direction, temperature-change and girth-convention errors, correct a constructed take-off, and record the evidence of a calculation.

12 min · 11 slides · 9 questions

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Slide 1 of 11

Three slips in lengths and factors

Plan length ordered for a sloped edge: a 16 ft plan run at 6:12 needs 17 ft 10-11/16 in, so the plan length is 22-11/16 in short.

A rounded factor: 42 ft is 12.8016 m with 0.3048, but 12.81 m with 0.305, which is 0.0084 m too long.

Rounding early: 20.25 ÷ 12 rounded to 1.69 first gives 19.54 lb.

Unrounded, it is 19.51 lb.

Correct and incorrect: true length, exact factors, rounding onceThree pairs of correct and incorrect calculations. A 16 foot plan run at 6:12 needs 17 feet 10-11/16 inches of metal, and ordering 16 feet comes up 22-11/16 inches short, drawn as two lines under a sloped red line. 42 feet is 12.8016 metres with the exact factor, not 12.81. A weight is 19.51 pounds if rounded once and 19.54 if rounded early.Three slips and their correctionsSloped edge: 16 ft plan at 6:12Order 17 ft 10-11/16 inthe true lengthOrder 16 ft, the plan length22-11/16 in shortplan: 16 ftred line: true lengthdashed: 16 ft piecenot to scale22-11/16 inshortExact factor: 42 ft to metres42 × 0.3048 = 12.8016 m42 × 0.305 = 12.81 m0.0084 m too longRound once, at the end20.25 ÷ 12 × 10 × 1.156 = 19.51 lb1.69 × 10 × 1.156 = 19.54 lbrounded 20.25 ÷ 12 firstExample inputs, not an AFS job

Three pairs of correct and incorrect calculations. A 16 foot plan run at 6:12 needs 17 feet 10-11/16 inches, and ordering 16 feet comes up 22-11/16 inches short, drawn as a dashed short piece under a sloped red line. 42 feet is 12.8016 metres with the exact factor and not 12.81. A weight is 19.51 pounds if rounded once and 19.54 if rounded early.

Example inputs. In each pair the first row is the correct method and the second the slip.

Sources

Glossary

Floating-point error
The tiny error from storing most decimals in binary. 50 × 1.1 comes out as 55.00000000000001, so a plain round-up gives 56 instead of 55 unless the result is rounded to a set number of decimals first.
Intermediate rounding
Rounding a value in the middle of a calculation. It lets small errors grow, so NIST says to round only the final calculated quantity.
Reverse calculation
Working the answer backwards to the number you started with, such as dividing a weight back to the girth, to catch a slipped decimal or a wrong unit.
Take-off
The list of lengths, pieces and quantities worked out from a drawing before a quote or an order. Each line carries its unit and the factors used.