Math tricks

[mklotz]

I've probably lost half my potential audience by putting the word "math" in the title of this post; nevertheless most of what's here is simple enough that even the most rabid mathophobe shouldn't be frightened.


MENTALLY CONVERTING millimeters TO inches

The correct calculation is to divide mm by 25.4 (mm/inch) to obtain inches. 25.4 is close enough to 25 that dividing by 25 will come close to the right answer. Dividing by 25 is the same as multiplying by 4 and dividing by 100. So simply double the mm twice and move the decimal two places to the left.

Example: 73 mm => 4*70 + 4*3 => 280 + 12 => 292 => 2.92 in. (correct value = 73/25.4 = 2.87... in; 1.6% error)

Converting centimeters to inches is equally simple. A centimeter is 10 millimeters so proceed as above but move the decimal point only one place to the left.

Example: 31 cm => 4*30 + 4 => 124 => 12.4 in. (correct value = 31/2.54 = 12.20... in; 1.6% error)



MENTALLY CONVERTING meters TO yards or feet

To convert meters to yards we multiply by (39.37 / 36 =) 1.094 which can be approximated by 1.1. Multiplying by 1.1 is particularly easy; simply add one tenth of the value to the value.

Example: 123 m => 123 + 12.3 => 135.3 yards (correct value = 123 * 1.094 = 134.51... yards; 0.58% error)

A yard is 3 feet so one can first convert meters to yards and multiply the result by 3 or multiply the meters by 3.3 to obtain feet.

Example: 123 m => 3*100 + 3*20 +3*3 => 369 + 36.9 => 370 + 35.9 => 405.9 ft (correct value = 403.53... ft; 0.58% error)


MENTALLY CONVERTING kilograms TO pounds

A kilogram is 2.20462 pounds, which is close enough to 2.2 pounds for most purposes. As with meters-to-yards, multiplying by 2.2 is dead easy. Multiply by 2 and add the result with the decimal shifted left one place.

Example: 7.3 kg => 14.6 + 1.46 => 16.06 lb (correct value = 16.0937 lb; 0.21% error)


ACCURATELY APPROXIMATING PI

Every home shop should have a scientific calculator with built-in trig functions and value of pi. If you're in a situation where all you have available is a simple four-banger then you can either memorize pi or use one of the integer approximations. In grade school you probably learned 22/7

22 / 7 = 3.14286 (error = 0.04%)

which is only marginally better than rounding pi to two decimals, 3.14, which has an error of 0.05%

However, for really good accuracy, approximate pi by 355/113 which has an error of only 0.00001% ! This is about as close to the real value as you can get with integers that are easily remembered.

If you still have trouble remembering those numbers, consider this mnemonic... Write pairs of the first three odd numbers - 113355 - and divide down the middle into two numbers - 113 & 355. Now, with these two numbers in hand, if you can't figure out which to divide by which to get a number close to 3, there's no hope for you.

[bruce.desertrat]

pi got engraved on my brain a long time ago: 3.14159 is generally good enough for most purposes.

I guess I was a new math kid, and I hit 'time to learn advanced math like trig' just as the world switched to calculators so I never had to learn any of the old school approximation tricks. My first calculator was had a fixed 2-place decimal point four function so I did become quite adept at keeping rack of the decimal point in my head.

Makes me really wish that the pirates hadn't stolen Thomas Jefferson's metric references https://www.washingtonpost.com/news/...=.3a4d0a7c4342 life would be a lot simpler if we were metric like the civilized world. :-P

[benkeller3]

Marv...
I like everything you do but sorry on this one. I am taking out my cellphone with the mm to inch and inch to mm converter

[thehomeengineer]

I am in the metric system well nearly! In the UK we have a mishmash of metric and American imperial (UNC UNF NPT etc.) and British imperial. We have metric and imperial tube sizes but still use imperial pipe sizes and threads (BSP BSPT) then some old stuff is the old (BSW and BSF)
In my opinion (for what it’s worth) the old BSW/BSF threads are by far the best just wish the metric system used the thread form (55 degree rather than 60 degree) Mr Whitworth certainly got this right. However, the metric thread system is so easy to understand: simply take the pitch away from the outer diameter and that gives you the core size or if you like the drill size. This almost works for any metric thread (M8 x 1.25mm is an odd ball, A 6.8mm drill is recommended as a 6.75 drill is non-standard)
So not sure if we will ever have a full metric system
The Home Engineer

[mklotz]

I am in the metric system well nearly! In the UK we have a mishmash of metric and American imperial (UNC UNF NPT etc.) and British imperial. We have metric and imperial tube sizes but still use imperial pipe sizes and threads (BSP BSPT) then some old stuff is the old (BSW and BSF)
In my opinion (for what it’s worth) the old BSW/BSF threads are by far the best just wish the metric system used the thread form (55 degree rather than 60 degree) Mr Whitworth certainly got this right. However, the metric thread system is so easy to understand: simply take the pitch away from the outer diameter and that gives you the core size or if you like the drill size. This almost works for any metric thread (M8 x 1.25mm is an odd ball, A 6.8mm drill is recommended as a 6.75 drill is non-standard)
So not sure if we will ever have a full metric system

Folks will break a lot fewer taps if they use the form of the calculation that accounts for depth of thread...

TD = MD - DOT / (75*TPI)

where:

TD = tap drill diameter
MD = major diameter of thread
DOT = depth of thread expressed as percentage
TPI = thread pitch expressed as threads-per-inch

The simpler form of the equation...

TD = MD - 1/TPI

sets DOT = 75 (%) which is often more than required. By using a lesser value the tap has less material to cut and so endures less strain. Tables of suggested DOTs as a function of material are available.

The metric form of the equation is...

TD = MD - DOT*P / 75

where:

P = thread pitch

[mklotz]

Marv...
I like everything you do but sorry on this one. I am taking out my cellphone with the mm to inch and inch to mm converter

The real thing to take away from my post is how I adjusted the correct calculation into a calculation that could be done mentally without too much difficulty. I chose metric-to-inferial conversions as examples that would be frequently useful but the real hint is in the math tricks, not the problem on which they are used.

If you're already comfortable with math, the tricks won't come as any great revelations. OTOH, my experience on DIY fora suggests that math facility is not terribly common so tricks may be appreciated.

[ranald]

Thanks Marv, the big thing for those who do not like math it is a great double check like measure twice & cut once (especially in wood where we cant weld a bit on. Thanks for the 113355 as I had not seen that before: when at school we had to use tables and calculators were a very new item not allowed in exams.

Regards, Ranald (woodie that enjoys inginuity in metal & wood)

[Mi Tasol]

I've probably lost half my potential audience by putting the word "math" in the title of this post; nevertheless most of what's here is simple enough that even the most rabid mathophobe shouldn't be frightened.

For those who have to convert from inFerial to easy measurements

MENTALLY CONVERTING pounds to kilograms - divide by two and take away ten percent. 100lb / 2 = 50 - 5 = 45kg instead of 45.4kg - error is 0.009%

MENTALLY CONVERTING long tons to tonnes - treat as the same because one tonne is 2204pounds and the long ton is 2240lbs - error is 0.016%

MENTALLY CONVERTING short tons to tonnes - deduct 10%. One short ton is 2000 lb. 2000-200=1800lbs = 0.9 tonnes. Or 1.0 - 0.1 = 0.9 Error is 0.007%

MENTALLY CONVERTING feet to metres.
Larger measurements -Ten feet is 120 inches Three metres is 118.11 inches so calling ten feet three metres has only a 0.016% error.
For smaller foot measurements multiply by 300. One foot = 300mm, two foot = 600mm etc again has only a 0.016% error.

[ranald]

In early 70's I was required to do all metrification of Brisbane City Council goods in stock and for direct orders. there were about 10,000 items such as sheets of steel & timber, bolts, screws, pipes, Fms, Rhs, rod dowel, etc etc.Interestingly I'm still often asked area conversions such as how many perches is 10005 metres square or as many say 10005 square metres which has nothing to do with this discussion here but it helps to keep my grey matter not loose too much as I advance in age. LOL. My dad, a retired builder) passed away a couple of years ago(101 years) but previously continually asked me questions like how many feet & inches is there in 2.4 metres=older folk had trouble "visualising" the very easy metric system. I do have to think about the answer nowadays but I apply it as mental double checks when working with measurements. I have read the controversay in the UK and if anything like here the US & Uk will experienve this scenareo for many years to come.

"The powers to be" here decided to do an instant change (enforcing the law) forgetting about the repairs to buildings for example that required imperial sheets of plaster, plywood so they eventually realised their fopare and then changed laws to allow imperial (eg: 2.44 m sheets of ply as these were easily cut down to 2.4 m where a 2.4 metre sheet can never replace a 2.44 m sheet).

At the start we did not use cms much(now used in schools), only meters & mm, but in recent times we have adopted cms much more. Possibly for medical & policing matters eg: height of a person-- licenced driver like 178 cms (approx 5 ft 11 ins) is less confusing than 1766mm and so on & more accurate than 1.8 metres. Enjoy metric it's easier than imperial but don't keep dual measurement tapes and rules too long as eventually they become a pain in the butt or at least your eyeballs.

edit:- Also, I just looked at wikipedia which states (in the site I viewed) that perch is a measurement of length where in fact it is a measurement of area used by surveyors.

Cheers, Ranald

[editor@glue-it.com]

I decided to share my spreadsheet calculators - I'm gradually getting these into one workbook and have listed an early version on my pages here:

Workshop Calculator – glue-it.com

If you want a specific calculator added then let me know and I'll see what I can do