[USMA:34986] Converting and rounding

[Stan Jakuba]

This may be of general interest on this topic - pages from my training course handouts. It is intended for mechanical design engineers, and thus in pretty in-depth.

Stan Jakuba


To: "U.S. Metric Association" <usma@colostate.edu>
Sent: 05 Oct 22, Saturday 22:27
Subject: [USMA:34981] Re: metric converters

----- Original Message ----- From: "Daniel" <[EMAIL PROTECTED]>

This is sort of what I was getting after in the first two paragraphs of my post in USMA34970:

Conversion translators need to be smarter then just converting two numbers
by a conversion factor.  They need to do some sensible rounding using the
principle of significant figures.  In the example below, there is 2 feet

implies an accuracy much more then the original intent.

If a number like 2.000 feet were entered I could see a need for a result
like 60.96 cm.  But when a number like 2 feet is entered, then the result
should be rounded to the same number of significant figures and intended

see that this still is more accurate then the original.  Thus, the result
can be further rounded to 60 cm and maintain the same level of accuracy.




Dan





To: "U.S. Metric Association" <usma@colostate.edu>
Sent: Saturday, 2005-10-22 16:55
Subject: [USMA:34977] metric converters

with one digit and an answer in centimetres with 4 digits. Thus the result accuracy. Since the result, if rounded to two digits would be 61 cm, we can The precision could be determined from the number of digits to the right of the decimal point if the number entered is decimal. Entering a number like 5.5 would be treated with the lowest precision compared to say 5.500. Numbers in fractional form would have to be converted mentally to decimal and the user would have to determine the number of significant digits to enter. ----- Original Message ----- From: "Bill Hooper" <[EMAIL PROTECTED]>

On 2005 Oct 22 , at 1:13 PM, Pierre Abbat wrote:

On Friday 21 October 2005 18:02, Jim Elwell wrote:

We are re-doing our web site, and it has been suggested that we
provide a link to a web page that does conversions.

time until November.

I suggest that, if you can't find one, you put one on your own site. If you need help with the programming, I can write PHP, but probably won't have the

I guess they way such a converter would have to work this way:







Regards,
Bill Hooper
Fernandina Beach, Florida

P.S.
















--
No virus found in this incoming message.
Checked by AVG Anti-Virus.

The user must input the amount including the unit and MUST ALSO INDICATE THE PRECISION with which that amount is known. That would allow the conversion to be made and rounded off to an appropriate number of significant figures. In decimal representation it is easy to write numbers so that their precision is clear from the way the number is written. Since metric is decimal, it is easy to do this in metric. Could you avoid requiring the user to enter the precision and rely on his or her entering the starting value in such a way that the precision is obvious from the stated value? Yes, that can be done easily in metric. However, there are several reasons why I don't think that would work, especially with Olde English measurements. I've detailed a couple of these reasons in a long PS below if you are interested. Reasons why it may not be possible to know the precision of a number just by looking at the way people write it: (1) People entering amounts in Ye Olde English system might enter amounts in common fractions (or mixed numbers). If they know the precision is 1/16 of an inch (for example) they would write the value to the nearest 16th. But if the fractional part happened to be 8/16, he or she would almost certainly reduce that fraction to "lowest terms" and write it as 1/2. So, now would we know that it had a precision of plus or minus 1/16 inch or would we misunderstand and think the precision was only plus or minus 1/2 inch? A precision of 1/16 in. is about 2 mm while a precision of 1/2 in. is over 10 mm. Rounding the answer to the nearest 2 millimetre is not the same as rounding it to the nearest 10 mm. (2) Many people don't pay any attention to the precision of the numbers they use. If they measure something very carefully to the nearest tenth of an inch and get a result of 14 ft. 0.0 in., they would most often write just 14 ft. So how are we to know that the precision of this value is plus or minus 0.1 inch when it is written so it appears to be plus or minus a foot? (3) Sometimes people really need a conversion to as many decimal places as possible even though they do not plan on using them all. Even though they say they want a conversion for 3 feet into millimetres, they really mean that they want to know what it is regardless of whether the "3 ft" is plus or minus a whole foot or whether it is a value that is very precisely known to the nearest thousandth of an inch? These people may be people who are quite familiar with precision and know how to round off a very precise value to the appropriate amount depending on the precision he or she wants or needs. They want a precise value that they will then round off properly even though they want to enter an amount that appears not to be too precise. Do we give them the answer 900 mm, which is good enough and consistent with a precision of plus or minus one foot, or do we give them an answer of 914.40 mm which is consistent with a precision of a thousandth of an inch? (4) Some people don't know anything about precision and how to indicate it with the numbers they write. These are the people that will calculate 1.3 as a decimal and get 0.3333 and then multiply that by 3 and get a final answer of 0.9999. Version: 7.0.344 / Virus Database: 267.12.4/146 - Release Date: 2005-10-21

Conv&Round2.doc
Description: MS-Word document