Why Use Fractions?

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CPCaballero

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Why would anyone in the machining discipline specify dimensions in fractions? Elmer (in his classic ELMER'S ENGINES) for example uses fractions. Has there ever been a lathe or a mill or a micrometer (before digital) with fractional dials? You have to convert, say 7/64 to 0.109375 or 5/32 to 0.15625. How is anyone going to turn down a piece to 0.1093755 or mill a slot to 0.15625? I suppose that if you're within 0.0005 you're likely "close enough". However, you have to convert which is annoying and cumulative rounding errors could creep in if you're not careful. Also, why not be consistent and use only, say 64ths, rather than mixing 4ths, 8ths, 16ths, 32nds? Yes I know that 6/64ths is an "improper fraction" but at least you would have a single multiplier to remember. Did machinists work this way at one time, converting fractions to decimal? Why?

Thanks for your answers.
 
CPCaballero said:
Why would anyone in the machining discipline specify dimensions in fractions? Elmer (in his classic ELMER'S ENGINES) for example uses fractions. Has there ever been a lathe or a mill or a micrometer (before digital) with fractional dials? You have to convert, say 7/64 to 0.109375 or 5/32 to 0.15625. How is anyone going to turn down a piece to 0.1093755 or mill a slot to 0.15625? I suppose that if you're within 0.0005 you're likely "close enough". However, you have to convert which is annoying and cumulative rounding errors could creep in if you're not careful. Also, why not be consistent and use only, say 64ths, rather than mixing 4ths, 8ths, 16ths, 32nds? Yes I know that 6/64ths is an "improper fraction" but at least you would have a single multiplier to remember. Did machinists work this way at one time, converting fractions to decimal? Why?

Thanks for your answers.
Click to expand...

There was a long series of articles and letters to the editor 100 years ago in American Machinist magazine about this very thing. You can find a lot of this stuff on the internet, or download the magazine from Google. The gist of it was opposition to the metric system and use of decimal points. Back then, obviously, calculators weren't available, so they wanted an easy way to add and subtract dimensions. As a woodworker as well as a machinist, I can understand why fractions help out. With a common denominator of 64, adding and subtracting fractions in your head becomes second nature. My enter key isn't working, so pardon no paragraphs. Also, they didn't like the granularity multiples of ten gave. For example, 1/10 to 1/100 is a big change. I can't remember the name of the editor (who wrote the article) but the article explained why they liked fractions and inches so much better. It was a convincing argument.
 
I have an old Starrett caliper from my Dad which is vernier to .001" on one side and 1/64" on the other, so yes, such things did exist.

Having stock sizes in 2x increments is useful, 1/16, 1/8, 1/4, 1/2, etc., is useful. As an engineer all my drawings are dimensioned in decimal inches but the actual numbers are even fractions (.125, .250) wherever possible.
 
Fraction drills and sizes were the standard for U.S.A. measurement and carried on from building log cabins to building machines.

Holding +/- .001 on say the length of an engine block casting would make the price very expensive.

Before world standardization it was common to have part prints with leaving off all the unnecessary limits with a simple code that was easy to draw (part prints) and to understand.

Fractions allowed 1/64 error so that could be accomplished with a pocket scale (ruler). That allowed cut off and the like to be done with not using expensive measuring tools or requiring lay-out of every simple line.
(I believe for carpenters fractions gave 1/16)
Two place dimensions .00 gave +/-.010 so this could be measured by hand or with a precision measuring device but the set up could be some what loose.
Three places .000 required holding .001 and closer than that were often shown with a size and limits or with .0000.
This allowed simple drawings and sketches to accomplish manufacture of parts.

Most good toolmakers, machinist and carpenters knew fractions above 1/64 by heart (memory).
It was easier to remember tap drill sizes with knowing fractions.
Fraction were thought to be good because one could remember the thread size and the tap drill size with not having to consult the chart or book to remember size.

Many thought we had both worlds of measure with having fractions for simple and 1/10, 1/100 and 1/1000 and 1/10000 for close.

But things change and now with CNC and computers numbers can be more exact for all numbers when in the shop but out in the field simple might still be good.

Buck
 
When cut steel bar stock that I will saw on the hacksaw using a rough measurement with a tape measure and I shoot for right on with a pencil or magic marker always cut it long by a 1/8 to a 1/4' I use a .001" Micrometer to measure when I am machining. I Eye ball the .0001's on the mic scale and a .0001" reading mic and sometimes a pressure mic when I am grinding . I use a .0005" indicator to rough in a part when scraping and a "0001" or .00005 indicator when I am scraping super precion. I have tried to learn metric, as it would probably be less complicated in he long run but I was educated in the inch system and It's hard to teach this old dog new tricks. I also use a fractional tape measure wood or other non precision things like the other night when the wife had me measure a widow so she could order a blind.. Rich
 
Beyond the good advice about using measurements appropriate to the task and materials, there are good practical reasons for working in fractions rather than the "new fangled" decimal approach.

It is highly accurate. Not to be confused with precision. Fractional portions are discrete units. 1/3 is a good example. It is exact. The decimal value changes with the precision of the calculations: 0.333 != 0.33333.

It makes it easy to divide and multiply many numbers. A few common factors and you can convert most measurements in your head. You can do it very accurately without precision instruments. With a straight edge marked with even divisions, you can very easily mark off fractions in arbitrary number of divisions. For example, if you want a piece divided by 5, just put the beginning mark on one edge of the stock and the 5th division on the other side (not my image, just snagged from a google search :) )

woodequaldivide.jpg

It makes it easy to find reciprocal amounts. 1 - 1/64 = 63/64

Whether the underlying units are Metric, SAE, furlongs, chains, fathoms, or cubits, units don't matter. Fractions are based on a different philosophy of work. Mostly arising from the use of simple geometric construction that is basically without units such as dividing a line or an angle with a compass and straight edge.

As to the decimal being easier to convert than fractions, that is a strawman argument. Yes, you can easily convert Kilometers to mm or inches to feet. Big deal. You will not be working with multiple units on the same project and the conversion is not going to be needed. Chemistry is about the only area where you might work with things that are many orders of magnitude apart.

woodequaldivide.jpg
 
I love this site, and thanks for posting the pic :) It always drove me crazy to try to figure out how to dived something into multiple equal bits, but just seeing that pick blew my mind :). May seem really simple, but thats why I love this site, I learn new stuff all the time :)
 
I come to this site daily hoping to learn something and BINGO, you fulfilled the need. What a great, straight forward, simple, wonderful, obvious, idea. Can you tell I am excited? I can move on now. Thank you, I will spread this one around. Too simple!
 
Why use fractions? One reason is that you need to work with other guys who do.

I have one cute example of fraction craziness. For the last 40 or so years, I've done "in the field" warranty work for the Martin Guitar Company, and they express the action (distance from string to 12th fret) in thirty seconds of an inch as a fraction - specified as 3/32 under the first string, and 4/32 under the sixth.

After a generation or two at that spec, the company decided to lower it by 1/64 on both sides, so now it is expressed as

"two and a half thirty-seconds" and "three and a half thirty-seconds".

Here in the shop we use a shorthand: written as, "2.5 / 3.5" or spoken, "two 'n half three 'n half."
 
Excuse me, but EHHH... WHAAAAAAAAAAAAAAAAT???

Man that ruler trick was beyond awesome! Never in my life I had seen anything like that. It will definitely prove pretty useful! Heck, I can already see others watching me do this think I am some sort of magician with mighty druid like powers. heh heh heh

There should be a book with arcane tips and tricks like that! I bet that is not the only one most of us don't know...
 
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