Electronic calculator, significant digits

Special Note on Significant Figures Electronic calculators do not keep track of significant figures at all. The answers they yield most often have fewer or more digits than the number justified by the measurements. The student must keep track of the significant figures ... 

The manipulation of significant figures in multiplication, division, addition, and subtraction is important. It is particularly important when using electronic calculators which give many more digits than are useful or significant. If you keep in mind the principle that the final answer can be no more accurate than the least accurate measurement, you should not go wrong. A few examples will demonstrate this. 

If we just leave the answer the way our electronic calculator gives it to us, anyone could assume that the measurement had been carried out with a precision of 1 part in 86,387, which is not true. We must reduce the number of significant digits in the answer to two because the factor with fewer significant digits has two. Thus, we change the answer to 86 cm. ... 

The answer is 3.00 g/cm. It must have three significant digits because both the dividend (4.92) and the divisor (1.64) have three significant digits. In this case, add two zeros to the answer given by the electronic calculator (3) to get the correct number of significant digits. 

In general, electronic calculators do not give the proper number of significant digits. 

An electronic calculator gives its answers with as many digits as are available on the display unless the last digits are zeros to the right of the decimal point. The calculator has no regard for the rules of significant figures (see Section 2.4). 

Warning Electronic calculators do not consider the rules of significant digits. If they give the proper numbers of significant digits, it is just by chance. 

All digits in the coefficient of a properly reported value in scientific notation are significant, because the exponential part of the number gives the magnitude. The electronic calculator will do the arithmetic with numbers in scientific notation, but we still have to know how the process works because the calculator does not consider sigrrificant digits. See Section 1.3 for a discussion of calculator processing of numbers in exponential form. 

The use of an electronic calculator generally produces more digits for a result than are justified by the rules of significant figures on the basis of the data input. For example, on your calculator,... 

With an electronic calculator, it is easy to obtain a long string of digits that must be rounded to the correct number of significant figures. The rules for doing this are the following ... 

Finally, significant advances in the techniques of both thermal and thermochemical measurements have come to fruition in the last decade, notably aneroid rotating-bomb calorimetry and automatic adiabatic shield control, so that enhanced calorimetric precision is possible, and the tedium is greatly reduced by high speed digital computation. Non-calorimetric experimental approaches as well as theoretical ones, e.g., calculation of electronic heat capacity contributions to di- and trivalent lanthanides by Dennison and Gschneidner (33), are also adding to definitive thermodynamic functions. 

Sigma molecular orbital. A molecular orbital in which the electron density is concentrated around a line between the two nuclei of the bonding atoms. (10.7) Significant figures. The number of meaningful digits in a measured or calculated quantity. (1.8)... 

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