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Fractions are a Royal Pain in Imperial

fractions
Educational school chart from 1890 by R.O. Evans & G.A. Bass

What is a fifth of an imperial yard?  Answering that question requires a bit of math. 

Most likely the person asking the question expects the answer in familiar fractional inches where the fraction is some multiple of 1/2, 1/4, 1/8, 1/16, or 1/32.  Below are the simplest possible steps to convert 1/5 yard into proper fractional inches. 

ValueStep
1/5 yard What's 1/5 of a yard?
36/5 inch Multiply by 36 to convert to inches.
7 inches + 1/5 inch Extract whole inches for simplicity.
7 inches + 1/5 inch × 32/32 Assume at most 1/32 precision.
7 inches + (32×1/5)/32 inch Solve for the numerator.
7 inches + 6.4/32 inch Do math to calculate numerator.
7 inches + 6/32 inch Round to nearest 1/32 of an inch.
7 inches + 3/16 inch Reduce fraction for convenience.
7 3/16 inches Presto! We have the proper fractional inch answer.

Below are the answers for other common imperial lengths.  Can you do the math required to get the correct answer? 

Imperial QuestionAnswer
What's 1/5 of an inch? 3/16 inches
What's 1/5 of a foot? 2 13/32 inches
What's 1/5 of a yard? 7 3/16 inches
What's 1/5 of a mile? 1,056 feet

Metric is easier by a country kay.  For example, there are 10 mm in a cm, so 1/5 of a cm is 2 mm. 

Metric QuestionAnswer
What's 1/5 of a cm? 2 mm
What's 1/5 of a meter? 20 cm
What's 1/5 of a km? 200 m

0.3333333333

Some imperial zealots obsess about 1/3 because they incorrectly believe that dividing by 3 is incompatible with metric.  When they pull the 1/3 stunt, simply ask them what's 1/3 of a U.S. dollar?  There's never been a world financial meltdown because someone couldn't do division on a dollar. 

Answering the 1/3 question in metric is not a problem.  Depending on the desired precision, the answer to what's 1/3 of a meter is either 33 cm or 333 mm.  Easy peasy. 

Even if you need to pull out a calculator, metric is still far less effort.  Let's say your measurement is 1,267 mm.  You punch 1,267 into your calculator and divide by 3, and you're done in one operation. 

fractions
Where are the tick marks for 63/100 of an inch? 😑 😀 🀬

The imperial equivalent is 49 7/8 inches, so you punch 7 into your calculator and divide by 8 then add 49 then hit equals and finally divide by 3.  You get 16.63 inches, but sadly your tape measure does not have tick marks for 0.63 of an inch.  Doh!  What a royal pain for something so trivial. 

The Proof Is in the Pudding

Fractions are such a pain in imperial that entire professions switched to incompatible "decimal" types of imperial units just to avoid imperial fractions.  Land surveyors use decimal feet.  Machinists use decimal inches.  Meanwhile, carpenters use familiar old fractional inches. 

ProfessionImperial UnitsCompatible
Surveyor Decimal Feet
MachinistDecimal Inches
CarpenterFractional Inches

The consequence of using imperial units is that surveyors, machinists, and carpenters cannot share each other's measurements.  Surveyors and machinists do math every day, and they choose to avoid imperial fractions not because they are too dumb to do fractions but because they are smart and need to be efficient. 

Time is money, and imperial is on the wrong side of the equation. 

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