## STOP! Using Fractions

If you have one of those dial calipers that readout in fractions…..THROUGH IT OUT! These are a crutch that will keep you from learning how to use decimals in your woodworking.

Fractions are fine for 3rd grade arithmatic, but they don’t work for furniture building. The smallest common fraction that we use is 1/64″. That fraction translates to 0.015625″. This is way too much for furniture joinery. If you try to fit a mortise and tenon or a dovetail joint to a tolerance of plus or minus 1/64″ you are going to end up with a piece of scrap. We must use decimals in our woodworking. A fraction is nothing more than an unfinished arithmatic example, 1/4 = 1 divided by 4 = .25, or 3/16 = 3 divided by 16 = .1875.

So let’s learn decimals. The standard increment in industry and engineering today is one thousandth of an inch. The thousandth is expressrd 0.001″. In industry we commonly work to three decimal places. The first decimal place to the right of the decimal point is hundres of thousandths. Example 0.100 = one hundred thousandths, 0.200 = two hundred thousandths, etc., etc., etc.. The second decimal place to the right of the decimal point is tens of thousandths. Example 0.010 = ten thousandths, 0.020 = twenty thousandths and so on. And of course we already know that the third decimal place to the right of the decimal point is thousandths. Therefore, 1/8 = 1 divided by 8 = 0.125 or one hundred twenty five thousandths, 3/16 = 3 divided by 16 = 0.1875 rounded to 0.188 or one hundred eighty eight thousandths. As you can see it is not difficult. We learned the alphabet, and the multiplication tables we surely can learn the decimal equivilents.

Keep your calculator as close as your measuring tools and use it to finish those unfinished arithmatic examples. Before you start a project go over the drawing and put the decimal equivilents beside the fractions and work with them, not fractions. If you do your own design write your dimensions as decimals. It may be awkward at first, but in time you will be converting most of the fractions to decimals from memory. Lose the fractions and take up their decimal equivilents and you will be a more accurate woodworker.

## About R & B ENTERPRISES

Professional furniture maker and restorer. Dealer and collector of vintage and antique woodworking tools.
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### 15 Responses to STOP! Using Fractions

1. Lex Terrae says:

Why not know and understand BOTH decimals and fractions? Ain’t too hard!

I noticed that you criticized fitting a tenon in a mortise at a tolerance of1/64th, but you didn’t tell us what decimal value would be appropriate. Does it really matter? Isn’t it more a matter of “fit and feel” than measurements?

It’s your blog and your opinion but I see your position as being only an opinion. Proselytizing if OK, but don’t expect everyone to accept your choices.

• Once you learn and become comfortable with decimals your mind will automatically convert fractions to their decimal equivilant. Fractions are fine for framing and carpentry work, but they are too course for fine furniture.

My purpose is not to teach how to fit a joint, but to point out that fractions are too course for fine joinery.

Finally, you are right. The above article is my opinion. An opinion based on 47+ years in the machine trades.

2. Eric says:

Hi. I’m really enjoying reading your blog. You have a lot of good information. I agree with you regarding the decimals. It’s what I use in my woodshop. I have a question about your description. You say “Example 0.100 = one hundred thousandths”. Isn’t 0.1 = one tenth? Wouldn’t 0.001 = one hundred thousandth? Or am I backwards?

• Eric, thank you for interest in my blog. In elementary school arithmatic the number to the right of the decimal is tenths, but in the machine trades it is hundreds of thousandths. Thus 1/8 0.125 would be one hundred twenty five thousandths. The second number to the right of the decimal is tens of thousandths. Thus 1/16 would be 0.0625 or sixty three thousandths rounded up. The third number to the right of the decimal is thousandths in either system, but in the machine trades it is the basis for the system. If I haven’t cleared this up please ask more questions. I’m trying to pass on the knowledge I have so others can use it and benefit from it as I have.

3. Eric says:

I read this on another machinist website ‘”The shop trades have dropped the 10th and 100th divisions of an inch and refer to everything in thousandths of an inch.” Now it’s all very clear. And in the example I cited above, one-hundred-thousandth is the same quantity as one-tenth, just expressed in different nomenclature. So it all makes prefect sense to me now. And now I can talk to machinists in their lingo!

• Not only that but you now have a much clearer picture of fractions. A fraction is nothing more than an unfinished arithmatic example that when finished yields a decimal. Now you have learned “machinist language” for decimals you can easily work with decimals and talk to others and everyone will know what you are talking about. Decimals make working with fractions of an inch easy. Thanks for your interest. I hope you learned something useful.

4. lman1000 says:

Have you ever found a drill set labeled in thousandths? Every one I’ve ever seen has been labeled in fractions or millimeters. Even the mills in the machine shop are labeled in fractions. I’m all for thousandths, but I constantly need to switch my measurements in thousandths over to fractions to match up my tools. I like inches, but I don’t like fractions.

• Most drill indexes label the bits by fractions and decimals. When we were in school we learned the multiplication tables. The decimal equivalent of fractions is pretty much the same. If you do the math (1/4=1 divided by 4 = 0.250) the conversion is easy and after a time you will have the more common ones memorized.

5. You can definitely see your enthusiasm within the work you write.
The world hopes forr even more passionate writers like you who aren’t afraid to say how they believe.

• Thank you for you kind words. My main goal for this blog is to keep as much information on the finding, cleaning and restoration, and use of old tools as I can. This would help the next generation to know the value of these old tools.

There is a lot to be said for modern technology, but there will always be a place for our heritage.

6. fractions are not to course for anything. they may seem messy to you but they are just another way of representing the same thing. If you have difficulty moving back and forth then use the one you are comfortable with.

I don’t know of any way using one notation vs the other would hold either party back. industry, what industry? is by the way not really that big of a deal. no one buying the fruits of the labor here is going to care exact dimensions nor how they where derived. as for Engineers just leave them out. they use what is appropriate to them at the time and they are not woodworkers.

it would only be important if you where building half of a box on one coast and you friend the other half on the other coast. and even then it is not the method of notation but rather the degree of accuracy. 1/1000 or 0.001 always assuming that you are talking about the same measurement system. I mean you could mean 1/2 and inch and someone else could mean 1/2 a millimeter. does 0.5 millimeters make it better?

all of this is irrelevant. next people are going to say I can’t be 50% done with my project, nor can I say I am 1/2 (“one half”) way there must I be 0.5 way there (sorry, five hundred thousandths). it is just notation, relax and stop worrying about how accurate people are trying to be. let them do what they want and learn basic math for your self. You obviously know it so teach them rather than deriding them.

if I can’t use 1/64 at fifteen thousand six hundred and twenty five millionths (did I spell that right?, I am bad at spelling. It seams I am wrong five hundred thousandths of the time). can I use 1/32 at three thousand one hundred and twenty five, hundred thousandths? So I am assuming that 1/16 would be too accurate at six hundred and twenty five ten thousandths. (it is much easier to say, you have that) if thousandths is the root then ten thousandth (and several sixtheenths) are out. or perhaps I could say 1/2 of a thousandths, Oops, I mean five ten thousandths.

It seems to me that you are suggesting three things. One that people should not ever attempt to be more accurate than a thousandth of an inch, round or truncate. Two that they only and always refer to partial unit notation in the thousandths and finally that they never use a fraction (and by extension percentages, those are fractions you know). You seem to use two points to support your persuasive argument, One that fractions are somehow “kiddy math” or otherwise in accurate, non-functional. (this is complete hogwash and wrong) And, that some other people are doing it “this one way” (read: in thousandths) so we should all do that as well. Then you seem to be trying to drive the point home with the worrisome idea that the readers will be left behind if they don’t get on board with what you say. As far as I can tell all of this is more about your difficulty understanding numbers, and wanting to have it your way.

You may not find fractions comfortable to use but some of us are comfortable with both ways of expressing a value and have no difficulty moving back and forth. As for people just beginning, don’t discourage them from learning either system of notation. As others have said, learn both, it is not like it is rocket science it is just a little familiarity and effort.

I am sorry, I am thinking I am coming across to aggressive. Which is not my intention, though I am not going to change it, I suspect it is one of the issues with the way people where raised. Or rather the time in which, I tend (I don’t mean to be age-iest here) to think that older people or people who do lots of math are far more comfortable with fractions. Mainly because they are easier to do in your head. Decimal notation in math with big values get’s to be a lot to handle in your head but fractions are actually easy, well if you are used to not having a calculator around. Either way 0.5in or 1/2in as “you” pointed out they are just notation and either way no one is being held back unless they simply don’t know basic math in the first place. If that is the case let’s help them learn that math as opposed to telling them what not to do. By the way in all math the number to the right of the decimal point is the tenths position, their is no grade school math and adult math, it’s the same. so long as you have base ten it is the same stuff, base eight that is a different story.

• Dwayne, you have way too much time on your hands.

I have been in the machine trades long enough to know that no dimension is ever cut “dead on”. There is always a tolerance, either expressed or implied. The finest fraction commonly used is 1/64 or decimally 0.015625. Therfore, if a tenon thickness is expressed as 1/4″ the finest tolerance would be plus or minus 1/64″. This could yield a joint too loose to glue or one that won’t go together. If the thickness is expressed as 0.250″ the industry standard tolerance for a 3 place decimal is plus or minus 0.005″. This would yield an acceptable fitting joint.

• Okay, thanks for your response, first off no I am actually very busy, I take a moment here because I think this is an important issue and a miss understanding that I have seen in one form or another many many times.

Second yes all cuts are accurate to a tolerance only. as a matter of fact all dimentions are accurate to a tolerance only, this is a given in life, I agree but it is also irrelevant as this truth does not change when you change your notation, or even your tolerance.

You make two repeating assumptions that I don’t understand or disagree with. First the concept of “finest fraction commonly used” this is not true, they are numbers you use the numbers how you write it or work the math is irrelevant. Second you keep referring to “the industry standard” and there simply isn’t one. different industry has different standards. I have been associated with persons working on performance engines and their tolerances where 0.0001 of an inch. or 1/10000 if you prefer. (see how they just change from one to the other and are the same value) I my self used to work in heavy steel, we commonly used fractional notation and the tolerance was 1/1000 (or 0.001) that is plus or minus 0.0005 (5/10000) which was convent becouse most of our machines where calibrated to one ten-thousandths.This means when someone came to us and said make this piece 1/64 it had to be between 0.016125 and 0.015125 (0.015625 being the 1/64) and on our machines we would shoot for 0.0156. (because you round at the end not in the middle)

what notation you use does not force you to any tolerance. if you have a dial caliper that only marks in 1/64 that does not mean that has to be your tolerance (unless that is all you have), your tolerance is largely down to capability. Capability to make a cut and capability to measure the cut. I am assuming that you are not going to throw away your ruler or tape measure because it is not in decimal notation. no, you make / mark your 1/2 inch cut an when you measure it with your dial caliper in decimal notation you get 0.53 you know you are three hundredths out. wether you note it as a fraction or not is irrelevant.

The most accurate marked fence I have herd of commonly is the Incra LS stuff. Notice how it is marked on the fence rule in divisional notation (i.e. fractions). However the fine wheel adjuster is detented (it clicks) at 0.001 of an inch. You can and in fact do have both at the same time. Fractional dial calipers are actually new (I believe). it is easier (in general) for machines to work with the evaluated number (decimal notation) because of the idea that one measure measures a measure and another measure measures that et cettera. (wow that was confusing) if those are done in tenths of an whatever you get decimal notation (vernier caliper) fractional dial calipers are around because people use fractions and generally don’t need to specify a tolerance each and every time they use a number (yes there is one but it is implied) in one way fractions are cleaner as they defer your rounding or truncating to the final measurement.

you can work in both fractions and decimals at the same time. it is no different. I do really hope this has been helpful.

• If you had taken the time to read the about me page an intelligent person like yourself could have figured out what industry I refer to. Space does not permit explaining every detail. Some things must be left to the reader.

My blog is aimed at the average, maybe beginning woodworker/handtool user who has a measuring tape and maybe a fractional caliper. In this article I am trying to make the point that these are not close enough to measure joinery tolerances. And at the same time show them a measurement system that is easy to use and accurate. Since, to date, you are the only one to complain I think I accomplished my goal.

While you are right in that one can go back and forth from one measurement format to another I submit that for the average person who has not be exposed to measuring accurately his or her entire life as you were, this is confusing. Therefore sticking to one measuring format would be best. That said it is much easier, for the average person, to work with decimals than fractions.

As I said the intent of the article is to show those less experienced at measuring accurately an easy way to do it in their own woodshop. While everything that you say is accurate it is none the less confusing to those who have very little experience at this. It is my contention that it is best to pick a method of doing things and stay with that method until one becomes proficient at it. Then experimentation may lead to a method that works better, but at least it won’t be confusing.

This discussion has not be helpful. I believe it is confusing to the less experienced and rather pointless.

7. Steve says:

I managed a Machine maintenance department for 20 years (before retirement), and was trained originally as a machinist. I learned a long time ago that their are more machinist that are shade tree lawyers than in any other trade, and they will argue over the stupidest topics imaginable. I also managed the ISO documentation system for all of our “Standards” used in measurements. Everything was done in thousandths, or tenths of thousandths period. The caveat being metric which we normally translated into thousandths… except for a few of our younger engineers who thought in metric… And they all used decimals no one worked in fractions. Your original post was spot on, and I’m sure resonated with most craftsmen. Any one arguing about the topic such as your detractor could have expected transfer or early “retirement” from my company…There is no room for error in modern manufacturing in any discipline… That being said, in rough work, being overly critical of measurement wastes a lot of time and cost money. The Craftsman should know when to shift gears from plus or minus a 1/64 to plus or minus a 0.0001 (tenth). The ones that don’t, do not need us explaining it to them. They need to work at flipping burgers or go into politics…or some other useless minimum skilled occupation.