Converting fractions to decimals

[Ramon WilsonParticipant @ramonwilson3]

Ah I see now Michael

Ok you (all) have me convinced – well, sort of – but I still don't see the need to go there myself so I'll keep tapping those keys if only to give my fingers some exercise – what was it 'they' say about old soldiers – fading starts here I guess

I've a few years left as yet I hope but I guess I won't see too much spot changing in my future

All the best guys – Tug

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Nigel Graham 2 on 17/08/2021 17:38:13:

[…]

Not sure what the photographed umpteen-step example is on that theme… More like Strictly Come Dancing.

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It is, as already stated, the Fractional Calculator’s own explanation of its work.

The example quoted was trivial. … the App is [again, as already stated] capable of much longer calculations with fractions.

… I’m beginning to wish I hadn’t mentioned it.

MichaelG.

[Ramon WilsonParticipant @ramonwilson3]

Well – there you go part two! Thanks Nigel.

Something else learnt – had never seen or thought to do that before believe it or not but makes total sense.

So now own to Jason,s/Michael's 11 inputs but, if the 25.4 is in the memory it comes down to 9 – it gets less onerous per post!

See, a (basic) calculator is all you need after all

Apologies Michael

 

Tug

Edited By Ramon Wilson on 17/08/2021 17:58:16

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Ramon Wilson on 17/08/2021 17:57:14:

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Apologies Michael

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No apology needed !!

The opening line of my first post in this thread was :

I’m not taking sides… each to his own

MichaelG.

[JasonBModerator @jasonb]

Posted by Ramon Wilson on 17/08/2021 17:57:14:

 

So now own to Jason,s/Michael's 11 inputs but, if the 25.4 is in the memory it comes down to 9 – it gets less onerous per post!

 

Kind of brings up back full circle to the chart or a spread sheet. Dozen clicks to start with and then no more. How many times would you have to enter those 9 digits on a drawing like your triple? 100 maybe or more so that's 900 presses vs 12. Sheet or part sheet of paper on the desk infront of you takes up no more room than a calculator. And with that chart from the first post there is no need to add on the full inch dimensions or add multiples of the divisor be it in your head or with a calculator. Click image to get it larger.

Edited By JasonB on 17/08/2021 18:38:20

[Nicholas FarrParticipant @nicholasfarr14254]

Hi MichaelG, every day is a school day, so no need to regret mentioning it, if nothing else I've learnt a couple of different ways to use my calculator and it's been interesting to see the full fractional calculation of a simple sum. My late elder brother was really very good at maths and I can still remember him working out quite long and sometimes complex equations in his head while using a slide rule, my siblings and myself would turn to him for help if we were struggling with our maths.

Regards Nick.

Edited By Nicholas Farr on 17/08/2021 18:49:43

[SteviegtrParticipant @steviegtr]

Thanks for that Tim. Some good charts.

Steve.

[JAParticipant @ja]

Perhaps we could have a fractional micrometer?

The slide rule has yet to be put away but I am redrawing the model (to metric) using my own spread sheet.

JA

[duncan webster 1Participant @duncanwebster1]

Posted by Michael Gilligan on 17/08/2021 15:19:06:

Posted by duncan webster on 17/08/2021 14:46:06:

But I don't have a ruler or a caliper that has 80ths of a millimeter on it. Decimals on a calculator is the way to go every time for conversions unless you are on the cad.

 

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I presume that you write in jest, Duncan … But just in case: The point was that the fractional calculation is exact, and the decimalisation thereof is only done on the answer.

MichaelG.

but 40.8625 is exact, because 1/80 = 0.0125 exactly, so multiples are exact at 4 decimal places (or 3 for even numbers off). I was just making the point that 42 + 69/80 is a fairly useless dimension. Actually converting any number of 1/128" to metric gives a decimal number within the precision of my calculator, 25.4/128 = 0.1984375 exactly. In reality I'd use 0.20 as my DRO doesn't do better than 0.005

Yes there will be some situations where the decimal runs out of decimal points, but not model engineers converting imperial fraction lengths to metric.

Edited By duncan webster on 17/08/2021 22:16:08

[Ramon WilsonParticipant @ramonwilson3]

I was responding more to the comments on using calculators in response to Tims first post but I concede Jason (and Tim), that is a good chart.

One would still have to ammend the drawing annotation however (or refer to the chart each time) and use a calc to add accumulated dimensions – personally, I certainly couldn't keep something like that in my head so, as with so many things – it's down to choice – my initial comment was that I didn't see why using a calc was percieved as an issue. I'm afraid I still don't but certainly agree, that the chart that Tim suggests would be a useful addition to the workshop

I have a very nice small, hand held plastic coated chart – similar lay out to the Zeus chart but personally I find it quicker ? easier? to just punch what I want into the calc. Habit I guess.

Just the way I have developed working over these years – paying money and taking a pick springs to mind

Nothing about sides Michael just your line – … I’m beginning to wish I hadn’t mentioned it.

Apologies were for the further perpetuation

Tug

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Ramon Wilson on 17/08/2021 21:50:38:

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Nothing about sides Michael just your line – … I’m beginning to wish I hadn’t mentioned it.

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That was more a reaction to Nigel’s dig at me

… Water under the bridge

MichaelG.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by duncan webster on 17/08/2021 21:49:55:

[…]

.

I haven’t got the will to argue about this, Duncan

Like I said in the first place: Each to his own

I just thought people might be interested

… and, as I have already stated: The example was trivial … the App gets increasingly useful when you are doing more complex calculations.

MichaelG.

[Nick WheelerParticipant @nickwheeler]

Posted by duncan webster on 17/08/2021 14:46:06:

But I don't have a ruler or a caliper that has 80ths of a millimeter on it. Decimals on a calculator is the way to go every time for conversions unless you are on the cad.

I wonder how many people have machine dials or micrometers marked in fractions. That would mean boring that 11/64" hole to a +/- 0.0005" tolerance is always going to involve some futzing around with a calculator. Or a conversion chart – which gets harder to read the more complete it gets. Or log tables if you're some kind of luddite/weirdo/masochist.

My machinist grandfather offered this advice a long time ago: work in whatever units the drawing is dimensioned in – converting to your 'normal' increases your chance of cocking up. My machinist aunt repeated it a couple of weeks ago when we were talking about making stuff.

 

Edited By Nicholas Wheeler 1 on 17/08/2021 22:28:06

[SteviegtrParticipant @steviegtr]

Well i have worn a shallow groove across my workshop with the new Hemingways knurling kit. All in Imperial. Looking up how many thou is this size. Worst thing is i have no imperial drills , so had to order a shiny new set. + borrow imperial reamers from a friend. Not so cheap a job. But more stuff for the workshop i guess.

Steve.

[Bill PudneyParticipant @billpudney37759]

As a smart arse I have avoided all the angst by drawing everything that I make in metric, as I feel that inches, feet, fractions etc are best left in the realm of Ancient Oddities.

cheers

Bill

p.s.Basically though I agree with Tug……………..

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Bill Pudney on 17/08/2021 23:39:43:

As a smart arse I have avoided all the angst by drawing everything that I make in metric, as I feel that inches, feet, fractions etc are best left in the realm of Ancient Oddities.

cheers

Bill

p.s.Basically though I agree with Tug……………..

.

[ says the man who never does the job ]

MichaelG.

[Bill PudneyParticipant @billpudney37759]

[ says the man who never does the job ]

MichaelG.

Hmmm. Just as well that I'm not sensitive, have a look at my albums………….

cheers

Bill

[Ramon WilsonParticipant @ramonwilson3]

Michael said,

[ says the man who never does the job ]

I can only assume you are refering to yourself there Michael – yes the topic has run on a bit but it's promoted some good comment from all points of view.

Nicholas said,

My machinist grandfather offered this advice a long time ago: work in whatever units the drawing is dimensioned in – converting to your 'normal' increases your chance of cocking up. My machinist aunt repeated it a couple of weeks ago when we were talking about making stuff.

With high respect to your grandfather and aunt's no doubted machining skills I can't agree that this is the right approach. It should be the machine being worked on that sets the parameter. Using imperial dimensioned drawings on a metric dialled machine without converting the dimensions is a fraught experience and vice versa. It compounds itself if the measuring kit doesn't match too but as said DRO eliminates it down to personal choice of the system preferred

That's based on a lot of working experience of this very issue – jobbing shops always had a myriad of machines in both and of course a constant supply of drawings varying daily including yes even the odd few in fractions! It certainly enabled me to decide that metric was far the better system (for me) to work in and apart from the Z movement on my old Linley mill all working is done in metric. – I get round the Z movement by using metric slips and a dead stop and of course reverse conversion using, dare I say it, a calculator

Regards – Tug

[SillyOldDufferModerator @sillyoldduffer]

Posted by SillyOldDuffer on 17/08/2021 17:26:40:

Posted by Michael Gilligan on 17/08/2021 13:49:11:

Posted by SillyOldDuffer on 17/08/2021 12:03:49:

[…]

All fraction calculators suffer to some degree from this inaccuracy, though the more sophisticated versions do far better than simple minded digital calipers. Michael's example is close: his calculator (and Nick's) both give 1¹¹⁄₁₆ x 25.4 = ³⁴²⁹⁄₈₀. So does mine. However, the real answer is ⁹⁶⁵¹⁷⁷⁶⁹⁵¹⁴⁰⁸³⁹³⁷⁄₂₂₅₁₇₉₉₈₁₃₆₈₅₂₄₈. Don't panic, ³⁴²⁹⁄₈₀ is an excellent result, the error being only -²⁷⁄₁₁₂₅₈₉₉₉₀₆₈₄₂₆₂₄₀.

Highlights a serious problem with fractions because the level of inaccuracy of each calculation depends on the individual ratio and on the number of display digits available. […]

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You must try harder, Dave

The fractional answer is correct

…

Sadly it's true, I've cocked up AGAIN!

Sorry,

Dave

PS Nurse says bed with no supper tonight…

Feeling a little happier with my foolish self this morning because my mistake was trusting a calculator; ironic because my post was about distrusting calculators doing fractions.

I used Python because it supports Fractions and Decimals as well as floating point. Floating point arithmetic is super fast because the numbers are in binary, but this causes conversion errors. 25.4 is actually stored as 0.25399999999999998579×100, which can cause trouble in long complicated calculations.

Decimal numbers are exact – 2.4 really is 2.4 but they are slow.

In Python, I typed:

fd = 1 + Fraction(11,16)
fd = fd * Fraction(Decimal(25.4))
print( fd, fd.limit_denominator() )

which gives the slightly wrong answer 96517769514083937/2251799813685248, which was approximated by limit_denominator() to 3429/80

Doing the same sum in fractions throughout gives the right answer:

ff = 1 + Fraction(11,16)
ff = ff * ( 25 + Fraction(4,10))
print( ff, ff.limit_denominator() )

3429/80 3429/80

So my blunder was caused by whatever method Python uses to convert Decimal(25.4) into a fraction.

Although I dislike fractions intensely in engineering drawings, they are perfect for gear ratios: change gears and threads. In that context, Python's limit_denominator() function is good for finding approximations, for example:

Fraction(math.pi).limit_denominator(10) = 22/7
Fraction(math.pi).limit_denominator(100) = 311/99
Fraction(math.pi).limit_denominator(1000) = 355/113

The various methods discussed in this thread are just tools. Tug's calculator may be good choice for him but other tools are available, and could be exactly the right tool for others. Calculators aren't the ultimate calculating aid!

Spreadsheets are calculators on steroids, but harder to learn. Programming languages even tougher but can do almost any calculation. As I've demonstrated though, just like physical tools, the operator has to choose and use them correctly. Banging screws in with a hammer is rarely a good idea,

Dave

[Nick WheelerParticipant @nickwheeler]

With high respect to your grandfather and aunt's no doubted machining skills I can't agree that this is the right approach. It should be the machine being worked on that sets the parameter. Using imperial dimensioned drawings on a metric dialled machine without converting the dimensions is a fraught experience and vice versa. It compounds itself if the measuring kit doesn't match too but as said DRO eliminates it down to personal choice of the system preferred

Measuring equipment is the key to this, not the machines! We're lucky that we tend to make small stuff, and that equipment is cheap. My machines are metric because I think in metric, when an imperial part comes up I press the button on the digital caliper and use an imperial micrometer.

[Ramon WilsonParticipant @ramonwilson3]

Well, we'll have to agree to disagree on this Nicholas.

Size of workpieces is immaterial – like you my machines are all metric – now. I got so fed up of switching from lathe (imperial) to mill (DRO set to metric) I changed the cross and topslide leadscrews to metric. Though not quite so important if it had been possible I would have done the main leadscrew too.

Imperial drawing – metric machines – two sets of measuring kit? Yes, I have them both across a range of kit which hark back to those days (and early working ones too) but the imperial kit is virtually redundant and rarely sees the light of day.

Calipers, digital or standard are not what are used for accurate measurement in a machine shop. If you choose to do so that's fine but it's not for me. Measuring across a part in a lathe or mill with a pair usually leads to differing readings to take your pick from.

Sorry, can't agree on this one

Tug

[Ramon WilsonParticipant @ramonwilson3]

Dave wrote

The various methods discussed in this thread are just tools. Tug's calculator may be good choice for him but other tools are available, and could be exactly the right tool for others. Calculators aren't the ultimate calculating aid!

Well I wasn't saying they are Dave but, WOW, looking at your impressive layout and explanation I'm glad I do not share such questioning mathematical skills. That's not being dismissive but recognising them for what they are and the fact that such would have an effect on what I want to do – which is, of course, – machining

As from the start if I'm faced with an imperial drawing then it's a matter of converting the dims to metric beforehand. The drawings can then be worked from the off and one can settle into the job equally so. The usual readily available calculator is, and has been, more than capable to convert the dims to the accuracy that will be worked on in any home workshop on the basic home kit likely to be found in one.

My interest is to produce a piece of 'model engineering' – I've always sought to do so in the most accurate terms using the most simplest approach. So far I'd like to think that has worked well for me.

To someone however, who was a dismal failure at maths, that's an impressive ability you have there

 

Tug

 

PS Agree about the Hammer though 

 

Edited By Ramon Wilson on 18/08/2021 11:12:53

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Bill Pudney on 18/08/2021 08:20:50:

[ says the man who never does the job ]

MichaelG.

 

Hmmm. Just as well that I'm not sensitive, have a look at my albums………….

cheers

Bill

.

I was referring to the job of converting dimensions, Bill … and your own explicit statement.

I am in no doubt of your [determinedly metric] engineering ability

MichaelG.

.

P.S. __ I did look at your albums, last night

Edited By Michael Gilligan on 18/08/2021 11:57:13

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Ramon Wilson on 18/08/2021 08:40:25:

Michael said,

[ says the man who never does the job ]

I can only assume you are refering to yourself there Michael –

.

For the avoidance of any further misunderstanding : Please see my response to Bill

MichaelG.

[Howard LewisParticipant @howardlewis46836]

This looks be getting a little bitter and twisted, when we are taking of UNITS.

The same parameter can be dimensioned in whatever unit you like, Angstrom units, Light years, yards; rods, poles or perches; spans, or bricks, if that is what takes your fancy. Just depends on how many decimal points you are prepared to tolerate, even if you prefer duodecimal, or whatever..

Film speeds were measured in Hurter and Driffield, Scheiner, Weston, Gost, and ASA, all for the same material,

Before anyone says it, not all at the same time!

They are only units, you choose the one that suits best. Best to try to use the same units as other people, which is where Whitworth, Sayers, BSI and ANSI, etc came in.

Because my kit is all Imperial, I am an "Ancient Oddity" in all senses, but occasionally use Metric,WHEN IT SUITS.

My shop made Workshop Comparator incorporates 8-32 UNC, 5/16 BSW and half round 4 mm pitch 0.0625"deep threads, because

a ) the UNC and BSF fixings were available, and

b ) I wanted a coarse thread, and the lathe could be set to 4 mm pitch, into which I could match a 1/8" ball bearing..

They happened to be the horses that suited my courses, did the job, and do not need to be interchangeable with anything else….

Howard

[Author]

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