Communication Guidelines
Physics 1305 and 1307

Dr. Cox

rev. Aug. 2003

	"The French never care what they do, actually, as long as they pronounce it properly."
	- Professor Higgins, in My Fair Lady

While we do care what you do, we also care how you communicate it. You are university students; you are expected to have at least adequate (and, before you leave, good) communication skills. This document is about good practices in scientific communication, together with ground rules that I apply in grading situations concerning the work you show. Except for the first one, there is no particular order or priority among them. These statements are for the most part phrased as guidelines (using "should," etc.); when I am grading your work in physics they have the force of requirements (substitute "must," etc., mentally).

1. Instructions for a particular job, test, or problem take precedence over general guidelines such as these. Applicable laws, university regulations, and the like, as well as ethical considerations, are still higher priority (but should not be in conflict).

2. Significant digits:
    Physical quantities are expressed by giving a value (number), the appropriate unit, and an indication of accuracy or precision. In the laboratory or on the job, the appropriate level of accuracy should be evident from the nature of the data and/or the procedure leading to the result.
    The level of accuracy can be expressed in several ways: verbally, using qualifiers such as "about", "very nearly"; or explicitly, as in "13.42 cm +/- 0.06 cm" or "69.3 cm +/- 0.2%". However, the quickest way to indicate accuracy, and the one most often used in my lecture, is by correct use of "significant digits". (Note: this is not the same thing as 'decimal places'.)
    In expressing a result that you have obtained, all digits of the result that you are sure of, are significant. In addition, one (normally only one) digit that could be off, is kept as significant. (If being off in the last digit could carry over to a preceding digit, that in itself does not make the preceding less significant; '67.9 +/- 0.2' will still have two pretty-sure and one uncertain significant digits.
    In interpreting a given number, all given non-zero digits are presumed significant, as are zeros between non-zeros. Leading zeros, as in '0.23' or '.0057', are never significant. If there is a decimal point in the number, trailing zeros are presumed significant; if not, they are ambiguous. Thus '93.0' has 3 significant digits, as do '430.' and '0.0240', but 40 000 could have from 1 to 5. (Since scientific notation always shows a decimal point, it also removes this ambiguity about trailing zeros.)
    Significant digits allow a quick, but only approximate, application of the rule that a result is only as good as its inputs allow. In multiplication, division, power, and root arithmetic, an output will be considered entitled to as many significant digits as its least accurate input.
    However, in any calculations that are intermediate between raw or input data and final answers, arithmetic results should be carried through as if the data were considerably more exact than they are, if reasonably possible; this will reduce roundoff errors. Intermediate arithmetic results should always be carried to at least one non-significant digit, to reduce the possibility of significant roundoff error.
    In the lecture portion, only, of my courses, the following apply:
All given quantities are valid to three significant digits, unless more are shown. (Trailing zeros that would be needed to make that precision apparent will often be omitted to save some space.) If more than three significant digits are given for a quantity, it is to be treated as being more precise. Answers are to be given to the precision justified by the inputs, normally three significant digits, with the following exceptions: trailing zeros after a decimal point may be dropped, and one extra digit will be accepted if that allows all roundoffs (including intermediate) to be avoided.

3. Using power-of-ten notation ("scientific notation"):
    Notations such as '**' or 'E' for giving exponents are computerese; they are necessary in computer programs, e-mail, and other contexts where superscript is not available, but they are not appropriate otherwise. The same applies to notations simply copied from a calculator display, if they differ from standard notations for the same quantity.
    In final answers, a number multiplying a power of 10 should have exactly one significant digit before the decimal point.
    In final answers, 10^-1, 10⁰, and 10¹ should not be used (unless to maintain uniformity of format, as in a table); use ordinary notation. (In these cases scientific notation loses space and clarity, instead of saving it.)

4. Since metric prefixes were introduced in order to avoid large or tiny numbers, there is seldom a good reason to combine powers of ten and metric prefixes (following instructions in a test of ability to do conversions or to use powers, is the only good reason I can think of).
    In final answers, instead of a power of ten multiplying a prefixed unit, I expect you to convert either to a prefix indicating near the actual size with the appropriate number (not using power of 10), or to the appropriate power with the unprefixed unit.
    However, there are some exceptions: (a) Since SI units are built with kilogram instead of gram, therefore for purposes of this rule kilogram counts as an unprefixed unit while gram counts as a prefixed unit. (b) The list of metric prefixes has not always been as extensive as it now is; a number of usages became common, and are still accepted, involving using a power of ten either for still larger multiples of the largest, or for still smaller multiples of the smallest. then-current prefixed unit; thus, for example, large distances often use power-of-10 with km, despite the prefix, since the larger prefixes are not commonly used with meter.

5. If an equals sign appears connecting two expressions, the expressions must be equal, not just related. A common type of violation of this rule is of the form (the example being in a calculation of the volume of a rectangular box which is 2 m by 3 m by 4 m)
    2 m x 3 m = 6 m² x 4 m = 24 m³
Here the second equals sign is legitimate but the first one claims that 6 square meters (value on left) equals 24 cubic meters (value on right).
For the same problem, the possible sequence
    l w h = 2 x 3 x 4 = 24 m³
has two violations: l w h denotes a product of lengths, which does equal 24 m³, but neither of them equals a number, which the middle expression is.

6. In any normal physics formula, the labels denote physical quantities which have appropriate units. (For a few labels "appropriate units" is no unit; for these, this procedural rule will be hard to violate.) In any instance of the formula, some (occasionally none) of the quantities will have values substituted for the labels: these values must have appropriate units. The other quantities (on different occasions none) will still be denoted by the label, which indicates a quantity with units: any unit stated with those is therefore redundant and thereby incorrect.
Thus when the formula is F = m a, the appearance of either
            (m) (4.5)
or
            (5 kg) (a m/s²)
as an intermediate stage is incorrect in its units. (However, writing down 5 x 4.5, without any units, off to the side, if you prefer to do so to do the arithmetic, is permissible. The arithmetic part is a legitimate part of the problem which you may separate from the rest. The flaw in the objectionable forms is that the use of some units or of some physical labels indicates that you are still using the physics formula which involves the physical quantities; you are not yet just doing the arithmetic.)

7. Remember that in essentially all cases capital and lower-case letters have different meanings: be sure your penmanship distinguishes them to others' eyes, not just in your own eyes. (Partial credit depends on 'legible, correct' work.)

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