Calculations, scientific significant digits

Significant figures (also called significant digits) are an important part of scientific and mathematical calculations, and deals with the accuracy and precision of numbers. It is important to estimate uncertainty in the final result, and this is where significant figures become very important. 

Suppose you must do a calculation using the measurement 200 L. You cannot be certain which zero was estimated. To indicate the significance of digits, especially zeros, write measurements in scientific notation. In scientific notation, all digits in the decimal portion are significant. Which of the following measurements is most precise ... 

Most scientific calculators have a button labeled I log I and, in most cases, the number is simply entered and the log button is pushed to display the log of the number. Note that there is the same number of digits after the decimal in the log as there are significant figures in the original number entered. 

For the same reason, we frequently carry extra digits through the intermediate steps of a worked example and round off only for the final answer. If a calculation is done entirely on a scientific calculator or a computer, several extra digits are usually carried along automatically. Before the final answer is reported, however, it is important to round off to the proper number of significant figures. 

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. 

Chemical calculations often involve very large or very small numbers and a convenient way to deal with these numbers is the scientific notation. In calculations or measurements, every quantity must show the proper number of significant figures, which are the meaningful digits. (1.8)... 

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