Identity help please--old tuba?

[sailn2ba]

Anyway, it's arithmetic. . .not mathematics.

[Rick Denney]

This is really about conversion between inches expressed in two different fractional bases, just like if you needed to be able to tell someone what a .680 inch bore would look like on a classic English caliper. I would multiply .680 by the largest fractional denominator I care about - say 64, which is 43.52. Then I'd round to the nearest integer, 44, and divide that by 2 until it's odd: 44 divided by 4 is 11, so I divide 64 by 4 also, and viola, .680 is about 11/16. (But if I had cared about 1/128, it would be 87/128.) Or you could use a table.

That last step, where you simplify the fraction, may feel kind of weird for people who are used to dealing with measurements as decimal fractions. .68 is not just another way to say .680, but apparently no one makes such a distinction between 44/64 and 11/16?

I care about 1/128, if the number I'm looking at is .680. Because 11/16 is .6875, and that rounds to .688, or .69, neither of which is .680. If the person was happy with an approximation to a fractional inch, they would have stated it as such.

It's a matter of significant figures, something we used to learn about in school, and the difference between accuracy and precision. If a person writes a number down as .680, then those thousandths are import to them, else they'd have written down .68. And if the thousandths are important, then that 1/128 is 9 of them.

It's also enough so that a slide would not fit, which gets into the accuracy part.

When I want to convert decimal inches to millimeters, I divide by 25.4. The relationship between 25.4 and one inch is indeed exact, because it was defined that way. You need the precision when dealing with a bore, because a 17mm bore is .669 inches and if you use .680 the slide won't fit.

For bell diameters, though, I divide centimeters by 10 and multiply by 4. Thus, 50 cm is 20 inches. That approximation is within
1.6%--close enough for bell diameters.

And, since there are three groups of four inches in a foot, 3 meters nearly equals 10 feet, again with an error less than 2%.

Those are all easy conversions to make, even without a calculator.

Rick "thinking people who write numbers down have some responsibilities" Denney

[Donn]

.68 is not just another way to say .680, but apparently no one makes such a distinction between 44/64 and 11/16?

I care about 1/128, if the number I'm looking at is .680. Because 11/16 is .6875, and that rounds to .688, or .69, neither of which is .680. If the person was happy with an approximation to a fractional inch, they would have stated it as such.

It's a matter of significant figures, something we used to learn about in school, and the difference between accuracy and precision. If a person writes a number down as .680, then those thousandths are import to them, else they'd have written down .68.

Right - I mean, it's up to you to decide whether 1/128 accuracy is meaningful in the context of the actual measurement, but indeed that's the difference I alluded to between .680 and .68. I'm just saying, no one ever mentioned to me in school that we ought to be doing the same with fractions. 88/128 for example instead of 11/16.

[iiipopes]

Hmph. As we were taught in elementary physics class, the concept of "significant digits" applies. Off an inch on estimating bell diameter doesn't mean much. Off 2/1000 on valve clearances means a whole bunch. It depends on context.

[sloan]

When I want to convert decimal inches to millimeters, I divide by 25.4. The relationship between 25.4 and one inch is indeed exact, because it was defined that way.

"The meter was originally defined as 1/10,000,000 of the distance between the equator and either pole; however, the original survey was inaccurate and the meter was later defined simply as the distance between two scratches on a bar made of a platinum-iridium alloy and kept at Sevres, France, near Paris. More recently, it has been defined as the distance light travels through a vacuum in 1/299,792,458 of a second."
http://www.answers.com/topic/metre

See also: http://physics.nist.gov/cuu/Units/meter.html

1/2.54 = 0.3937007874, which is *precisely* but not *accurately* 0.39370.

Unless you refer to the "international inch", which was defined in terms of the meter (as opposed to the much more widely accepted "rule of thumb" based on the anatomy of certain royalty).
Comparing the royal thumb with the scratched bar of platinum-iridium leads to the conclusion that there are 4*10^1 inches to the meter.

It's always possible that the Tennessee state legislature will define "cm/in = 3" - which is both equally accurate and precise.

Ken "defining doesn't make it so" Sloan

[scottw]

BTW,shouldn´t there be another thread opened to discuss the internatinal mess of different measuring systems?

This thread was opened to find info related to a tuba,wasn´t it?


Kurt

THANK YOU,Kurt!