Converting decimal inches to the nearest fraction

Here is a simple way to convert a decimal inch dimension to a fractional dimension.

Divide the decimal inch dimension by 0.0156. Then round to the nearest integer. This will be the nearest 64th of an inch.

For example, say I have 0.400-inches. 0.400/0.0156 = 25.6. I round up to 26. This means I should specify 26/64. Now, this fraction can be reduced by dividing numerator and denominator by 2 so I get 13/32. 13/32 = 0.406 with is as close to 0.400 as you can get with a granularity of 1/64th of an inch.

Where did 0.0156 come from? It is 1/64.

If you wanted to get to the nearest 32nd of an inch, divide by 0.0313. The nearest 16th of an inch, divide by 0.0625. I hope you see the trend here. I'm just doubling the previous number.

Rick

Dividing by 1/64 is the same as multiplying by 64. Saves a step.

Set your calculator to return integers (a key sequence like "fix 0" on many calculators).

Then 0.4 * 64 on the calc will return 26 directly.

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Originally Posted by mklotz

Dividing by 1/64 is the same as multiplying by 64. Saves a step.

Set your calculator to return integers (a key sequence like "fix 0" on many calculators).

Then 0.4 * 64 on the calc will return 26 directly.

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Marv,

As someone who tries my best to find the simplest method, I sure blew this one!

Thanks,

Rick

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Originally Posted by rgsparber

Marv,

As someone who tries my best to find the simplest method, I sure blew this one!

Thanks,

Rick

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It happens to all of us so I'm very sympathetic. I can't tell you how many times I've gone down a parallel path on an analysis and ended up solving an arithmetic problem with calculus or similar.

Why not just convert to metric and be bloody well done with that ridiculous garbage ? :-)

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Originally Posted by greenie

Why not just convert to metric and be bloody well done with that ridiculous garbage ? :-)

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On my last project, I was reverse engineering a part. If I had measured in metric, it would have been the same number of digits as in decimal inches. If it had been designed using metric, I would have gladly carried that forward.

Your question did get me thinking. In a previous post I suggested marking my wrench set with integers that represented the number of 16ths of an inch. I could have done the same with this project but used 64th instead. I would have had dimensions of 26, 39, 40, and 58. No doubt this would have caused confusion.

I do own an "engineer's" tape measure. it has decimal inches and no feet. OK, not as good as metric but a lot better than inches, feet, and/or yards.

Rick

@Rick Thank you.

Once I got my lathe and mill, I realized that I needed to convert between fractional and decimal and sometimes metric more often than not, so I made spreadsheet with all the inch fractions in 1/8th, 16th. 32nd, and 64th, decimal, and metric equivalents; printed & laminated a copy and attached with magnets to my cabinet. I have another one with all drill sizes , including fractional, letter and wire gauge on once side and tap and drill sizes on the other. Now, If I am working on a project and my hands are an oily mess mess, I don't have to reach for my calculator or reference book.

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Originally Posted by greenie

Why not just convert to metric and be bloody well done with that ridiculous garbage ? :-)

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I find this humorous...

Judging from the Shand engine avatar and your use of "bloody", you probably live in the UK, where beer is still dispensed in pints and bathroom scales are calibrated in stones; road distances measured in miles. So, I have to ask...

Why not just convert to metric and be bloody well done with that ridiculous garbage ? :-)

Sorry Marv, I come from the Land Down Under and WE converted to Metric 50 yrs ago, best bloody thing the Aussie government ever did.

Started as an apprentice Machinist and had to learn the easy way, instead of that diabolical, infernal, stupid Imperial measurement, as I progressed thru my apprenticeship.

As a machinist I have never worked with only an integer in my entire career. Whether the dimension is 25+/-.03 mm or 1.000 +/- .001” it’s all kind of irrelevant to me. I’m always working with decimals regardless of any system. And with the popularity of cheap digital calipers I believe many HMT viewers are going down the digital path also. So this constant harangue about one system or the other is getting rather old.

The US has been metricized (one form or another) for more than 134 years! The commerce act 1886 legalized the metric system in all courts and commerce. Then a few world wars intervened. It’s not prudent to change your system of units when going to war and tremendous economic expansion after the war further disincentivized change. But in reality we are mostly metric without knowing it!

Photography, wine and spirits, medicine, US Military, have been fully metricized for more than 50 years! The last time I had a “hip flask” (1/5 pint) of whiskey was in the 60s. Nobody orders a “quart” of wine with dinner. Every kid in 8^th grade since the early 70s knows that a “key” is a kilogram of illegal drugs. All groceries are dual dimensioned and quite a few consumers now know what kg vs lb. means on a package of hamburger. Most don’t need the precision or simplicity of metrics so life will go on until economics becomes a force for change.

Since this thread is about converting measurements to and from inferial fractions, let me present a clever approximation for converting fractional inches to millimeters. The arithmetic is simple enough to do in your head.

Keep doubling numerator and denominator until the denominator is 256. Then the numerator divided by ten is the equivalent in mm with an error of only 0.79%.

Some examples...

13/64 = 26/128 = 52/256 -> 52/10 -> 5.2 mm (correct value = 5.159375 mm)

1&13/16 = 29/16 = 464/256 -> 46.4 mm (correct value = 46.0375 mm)