Model Rocket Math: Converting Decimal Inches to Fractional Inches

[brockrwood]

I use on-line calculators (and handheld calculators) a lot when making low power model rockets.

I am more familiar with length measured in inches rather than in centimeters or millimeters.

So I run a calculation that spits out a length in inches. But it spits it out in DECIMAL inches: 6.784 inches, for example, rather than the fractional inches, in powers of 2, that most rulers are marked in.

So, I have a length in decimal inches but I need it in fractional inches: 1/4 inch, 1/8 inch, 1/16th inch, 1/32, inch, 1/64 inch, et cetera, so I can actually measure that distance with the ruler that is marked in fractional inches.

(Note: There ARE rulers that are marked in DECIMAL inches. I have one somewhere, but I can never lay my hands on it when I need it.)

(Rats, I just found it! I guess I don't need to do this conversion after all...)



OK, but assuming I can't find the ruler shown above, how do I get a quick approximation of a length specified in decimal inches in fractional inches? Arithmetic.

Take the length in decimal inches. What is it? In our example, it was 6.784 inches.

Now, decide what fractional units you want to use as the maximum precision for the fractional units. Is it 1/8's of an inch? 1/16's of an inch? 1/32's of an inch? I cannot really distinguish anything less than 1/16" with my old eyeballs, so I will use 1/16's of an inch.

Multiply the length, in decimal form, times the denominator of the fractional unit (16 in this case).

So, 6.784 inches times 16 is 108.544.

108.544 what? 108.544 sixteenths of an inch.

Round that to the closest whole number. So that would be 109. 109 "sixteenths" of an inch.

Put the rounded number over the fractional unit denominator, like so: 109/16.

What does that mean? It means that 6.784 inches is about 109 16th's of an inch. That is the closest fractional inch measurement to the decimal measurement of 6.784 inches.

But I need INCHES AND 16th's of an INCH! Help!

Just divide 16 into 109. You get 6 inches with 13 left over. So the fractional measurement that is approximately 6.784 inches is 6 13/16 inches.

There you go!

Or just use the decimal ruler.

Or just use the metric system. Millimeters are nice and small. You can just use millimeters as your unit of length and stick to whole numbers.

 

[prfesser]

You only need worry about the 0.784. Multiply by 64, gives 50.176 or just slightly over 50/64. Both numerator and denominator are even, so divide both by two (do you really need a calculator for that?). Gives 25/32, so 6 and 25/32.

FWIW 25 is 2 x 12 1/2. 32 is 2x16. So it's a bit more than 12/16. Which is 3/4. So...slightly more than 6 3/4.

Let's go back to millimeters, it's a heckuvalot simpler....

 

[brockrwood]

You only need worry about the 0.784. Multiply by 64, gives 50.176 or just slightly over 50/64. Both numerator and denominator are even, so divide both by two (do you really need a calculator for that?). Gives 25/32, so 6 and 25/32.

FWIW 25 is 2 x 12 1/2. 32 is 2x16. So it's a bit more than 12/16. Which is 3/4. So...slightly more than 6 3/4.

Let's go back to millimeters, it's a heckuvalot simpler....

You know, Napoleon may have been a megalomaniac dictator who forced his will on the people of Europe, but the metric system? He NAILED that. Just divide everything by 10. You know. Like the number system we use? Sigh.

 

[brockrwood]

You only need worry about the 0.784. Multiply by 64, gives 50.176 or just slightly over 50/64. Both numerator and denominator are even, so divide both by two (do you really need a calculator for that?). Gives 25/32, so 6 and 25/32.

FWIW 25 is 2 x 12 1/2. 32 is 2x16. So it's a bit more than 12/16. Which is 3/4. So...slightly more than 6 3/4.

Let's go back to millimeters, it's a heckuvalot simpler....

Yes, 6.784 inches is a bad example. Too close to 6.75 inches (6 3/4 inches) to bother with converting. If you use 1/32’s of an inch as your “precision” then my example works a bit better. I never need to go beyond 1/32 of an inch in precision when playing with LPR model rockets. Except for body tube diameters. Sigh.

 

[kuririn]

Simplify.
Print a table of 1/16" gradations of an inch.
1/16 = .0625
2/16 (1/8) = .125
3/16 = .1875
4/16 (1/4) = .25
and so on up to 15/16".
Pick the measurement closest to your decimal value.
That way you don't have to do the calculation every time you come across a decimal measurement.

 

[brockrwood]

Simplify.
Print a table of 1/16" gradations of an inch.
1/16 = .0625
2/16 (1/8) = .125
3/16 = .1875
4/16 (1/4) = .25
and so on up to 15/16".
Pick the measurement closest to your decimal value.
That way you don't have to do the calculation every time you come across a decimal measurement.

OK maybe my eyes can see 1/32 of an inch. Just aim between the two hashmarks for a 1/16 of an inch. But 1/64 of an inch? Forget it. I will go cross-eyed.

As I get older, I need LOTS more light on my workbench.

 

[brockrwood]

Simplify.
Print a table of 1/16" gradations of an inch.
1/16 = .0625
2/16 (1/8) = .125
3/16 = .1875
4/16 (1/4) = .25
and so on up to 15/16".
Pick the measurement closest to your decimal value.
That way you don't have to do the calculation every time you come across a decimal measurement.

Found the table:

https://www.reade.com/reade-resourc...-to-mm-millimeters-conversion-chart-thank-you
All I have to do is scan down the table and find .7812. That is the value closest to .784. That is 25/32". Done. Thanks!

- Brock

 

[Funkworks]

One can always ask a an online thingy to do the work:
https://www.inchcalculator.com/inch-fraction-calculator/

 

[brockrwood]

One can always ask a an online thingy to do the work:
https://www.inchcalculator.com/inch-fraction-calculator/

But then, eventually, we end up like the people on the "colony" spaceship in WALL-E. ;-)

 

[roc_boy]

This is the best tool I've found. I printed it out and keep it in my workshop quick reference binder. It gets used a lot

 

[neil_w]

Tables like that are great, often much quicker and easier than using a calculator. That's why I created a table of target weights of every different size balsa sheet; don't want to be fumbling with a calculator when I'm weighing sheets.

 

[Blast it Tom!]

My seventh grade pre-algebra teacher made us memorize decimal equivalents of fractions for 1/8". Over the years I've learned 16ths. And of course from there it's pretty easy to get to the next 1/32 (.031) or even 1/64 (.015 as near as we'll ever need).
I pointed out on another thread that, when they figured out that the survey establishing the length of the meter as 1/10,000,000 of the distance from the equator to the poles was incorrect, James Watt suggested making the meter equal to 40 inches. I think had they listened to him the measurement world would be a much happier place today... maybe I'm wrong who knows?

 

[brockrwood]

My seventh grade pre-algebra teacher made us memorize decimal equivalents of fractions for 1/8". Over the years I've learned 16ths. And of course from there it's pretty easy to get to the next 1/32 (.031) or even 1/64 (.015 as near as we'll ever need).
I pointed out on another thread that, when they figured out that the survey establishing the length of the meter as 1/10,000,000 of the distance from the equator to the poles was incorrect, James Watt suggested making the meter equal to 40 inches. I think had the listened to him the measurement world would be a much happier place today... maybe I'm wrong who knows?

Make the meter the same as 40 inches? Gosh, life would be much easier!

 

[Blast it Tom!]

Make the meter the same as 40 inches? Gosh, life would be much easier!

Exactly. 1 inch would be 2.5 cm, not 2.54 cm. From there, mass and volume conversions probably would have been easier as well. I really haven't thought it through. Maybe not... a cubic inch would be 15-5/8 cubic cm, exactly, but using fractions with cc's seems a sacrilege! But Watt's thought was that the metric system would have had much greater appeal. I dunno... maybe it's due to having the Imperial system all my life, but I tend to think in halves, quarters, eighths, etc, and if you try that with a meter, once you get to an eight of a meter (125 mm), to go to a 16th you're into fractions of a mm, 62.5 mm to be exact. I suppose in many ways it's 6 of one, a half dozen of the other!

 

[bjphoenix]

So I run a calculation that spits out a length in inches. But it spits it out in DECIMAL inches: 6.784 inches, for example, rather than the fractional inches.

Are we making this too difficult? Or is it because I'm an engineer and I work with numbers all the time?
I look at 0.784" and immediately I see 3/4" plus 1/32", or rather 0.75" + 0.30", so in crude terms it is just 3/4", if you have a ruler with more marks or if you can pick between the 1/16" marks then this is halfway between 3/4" and the next 1/16" mark.
Most people can remember the decimal equivalents of the quarters- 0.25, 0.50 and 0.75. It's not too hard to figure out the decimal equivalents of the eighths- 0.125", 0.375", etc. From there if you remember that 1/16" is about 0.060 and 1/32" is about 0.030 you can get more precise.

That ruler you pictured is called an "engineers scale". It is used to measure on civil engineering drawings, with scales such as 1"=10', 1"=20', etc.

Back to the other discussion, if I have to do intricate measurements for rockets, I will often convert them to millimeters. I do this sometimes when I'm making fin templates- wrap a piece of paper around the airframe, mark where it crosses, take it off and measure to the mark, in millimeters, then divide the total by 3 or 4 depending on number of fins. It is easy for me to put 2 or 3 more marks on the paper then I have an easy way to mark the fin locations.

 

[Sandy H.]

I memorized the 16th's when I was young and know a handful of 32nd's that were used often. As mentioned above, 1/64 is 0.015"-ish, so when push comes to shove, I can get there fairly quickly.

As far as metric goes, I only think in millimeters or meters, never centimeters. I know 1mm is 0.03937"-ish, so 10mm must be a heavy 3/8". Similarly, 12mm is a light 1/2". Since we used 3/4" plate a lot in my work, I know that it is just a bit thinner than 20mm or kinda like 2X 3/8" or 2X 10mm. At the end of the day, you can do brain math pretty close for sanity checks with just a few of those memorized, but if you're really doing detail work, then you're likely to use a calculator, spreadsheet, chart or other tool instead of just relying on your recollection of stuff.

The one I really screw up all the time (much to the detriment of my 29/240 AT cases) is that my brain defaults to 3/32" being smaller than 1/16", which is obviously 100% wrong, but somehow I've managed to convince myself of this incorrect relationship such that I am wrong 100% of the time. As I know I'm wrong 100% of the time, I usually flip my answer in my head, however I must have convinced myself last time that 3/32" was actually bigger than 1/16", so I'm wrong again. I am 100% embarrassed by the number of times that I have made this mistake. I also pretty much always flip left and right, so I'd be a terrible Rally navigator. My wife knows that in general, if I say take a left, she should go right. If she tells me to go left, I usually take a right, which is wrong, as she knows which one is which.

Yet, I remember 11/16" is 0.6875", which is pretty smack-dab in the middle of 17/18mm. . .

Sandy.

 

[Hyak]

Uhmmmm can't one just do the math? Its not that hard... (You'll probably want a calculater of course.)

Boy, it's just to bad there is not a system of measure based on, oh, say the number '10' we could use here in the US. (I can divide, multiply, add and subtract by 10 all day long.... In my head even!)

Whoever invents usch a system could even system name the unit's in a manner that told one how many units were involved in a bigger unit....


Someday maybe someone will invent something like this........

 

[SecondRow]

I can't believe this thread has been up for almost 24 hours and metricrocketeer hasn't chimed in.

Like others, I just multiply the decimal part of the measurement by 32 (the smallest line I can make out on my ruler), then round. If the rounded number is even, I divide by 2 and make it 16ths, and so on. There's your fraction. The whole number stays the same and gets added to the fraction.

 

[dr wogz]

I still giggle at numbers like .784".. how important is that? will .75" do? or is 25/32" really important?

 

[brockrwood]

I still giggle at numbers like .784".. how important is that? will .75" do? or is 25/32" really important?

The irony is that some on-line calculators give you an answer in inches but in DECIMAL inches, instead of just giving you the answer in millimeters or centimeters, a DECIMAL measurement system.

High speed computers defeated the move to the metric system in the USA and in some other countries. The hassle of converting units went away now that we all carry powerful computers in our pockets.

 

[kuririn]

I still giggle at numbers like .784".. how important is that? will .75" do?

Someone eyeballing it wouldn't know.
BUT YOU WILL
Heh.

 

[boomtube-mk2]

All I know is that 3 inches equals 40 feet in N-Scale.

 

[Steve Shannon]

The first rule of converting between systems should be “don’t!” Just work in one system if it’s possible. Unfortunately, it isn’t always possible.
So, the second rule should be, always perform dimensional analysis. Carry all the units with you throughout any conversion. That will help you notice when you make an illogical conversion.

 

[John Kemker]

I have about three different rulers that measure inches in 1/100ths. I'll swap between them and metric at various times.

 

[dr wogz]

The irony is that some on-line calculators give you an answer in inches but in DECIMAL inches, instead of just giving you the answer in millimeters or centimeters, a DECIMAL measurement system.

High speed computers defeated the move to the metric system in the USA and in some other countries. The hassle of converting units went away now that we all carry powerful computers in our pockets.

Please, I am genuinely curious: why did high-speed computers defeat the move to the metric system? I haven't' heard this.. curious to the reason(s)..

 

[dr wogz]

Someone eyeballing it wouldn't know.
BUT YOU WILL
Heh.

Well, this is what I'm trying to teach some of our designers. yes, CAD will spit out .313" for a dimension.. (and per our default: 3 decimals = ±.005")

But (in this case) it's a handle, cut from 5/16" bar stock.. could it be .300"? or .35" Do you want it machined to .313±.005"

Call up the material spec in the material box, and make the .313" dim a reference dimension..


(What the #$%^&* is a "Reference" dimension?!?! )

 

[brockrwood]

The first rule of converting between systems should be “don’t!” Just work in one system if it’s possible. Unfortunately, it isn’t always possible.
So, the second rule should be, always perform dimensional analysis. Carry all the units with you throughout any conversion. That will help you notice when you make an illogical conversion.

As Air Canada found out the hard way during the Gimli Glider incident.

https://en.m.wikipedia.org/wiki/Gimli_Glider

 

[Hyak]

The first rule of converting between systems should be “don’t!” Just work in one system if it’s possible.

EXACTELY!!! Just use the metric system! Its EASY!!!! And in those PITA instances where you need to know the equivelant/conversion, whip out the calclator.

As to high speed computers, I had not heard that reason given before. I do know that back in the 80's (could have been late 70's as well) the US Govt tried to get everyone over to the Metric system. I vaugelly remember seeing speed linit signs in WA or CA that were in both KPH and MPH.

But, - and I *AM* an American for the record - the lazy American public got upset to the point where the Govt. gave up.
(I assume that industry fought it as well since probably no one wanted the expese to convert)

It yes it *IS* a pain to convert. (So dont. Just Learn It!) but had the US Govt. persereverd, no one nowadays would ever even think twice about it now. My kids would not ever know about the old, (IMO stupidly random system) They would have learned metric and that would be that.
(Actually my kids do know the metric system, and that's actually what they use And no, they are not scientists or engineers. I just made sure they knew it. Now its what they use)

I mean come on! It is SO SIMPLE, and in some cases almost intuitive.
For example: The freezing point of Water (@ STP) = 0c. Boiling Point= 100c Makes sense, yes? Imperail system....32f & 212f....huh?

Metric is also the SI system.... meaning 'International System of Units'
I dont *beleive* imperial units, which while still are used in other parts of the world, are considered part of the International Standard...could be wrong though..

Heck, even rocket Motors are physically sized using the Metric (54mm, 38mm, which is (5.4cm or 3.8cm) but not the rest of the rocket!

Ahhh I could go on on this one! But my advice, just learn it, and once you are used to it, you love it....

And its a very pleasent 23.4c here today...!

 

[kuririn]

As Air Canada found out the hard way during the Gimli Glider incident.

The infamous Mars Climate Orbiter comes to mind:

 

[boomtube-mk2]

As to high speed computers, I had not heard that reason given before. I do know that back in the 80's (could have been late 70's as well) the US Govt tried to get everyone over to the Metric system. I vaugelly remember seeing speed linit signs in WA or CA that were in both KPH and MPH.

I don't know about WA but for a time CA had those signs.

Personally I will never convert to the metric system. It is under 400 miles between San Francisco and Los Angeles but it is over 600 kilometers and that's just too danged far to drive!