Numbers significant digits

Rule II. The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing —10 after the result. 

When connecting numbers to logarithms, use as many decimal places in the mantissa as there are significant digits in the number. 

Numerical values of the constants that follow are approximate to the number of significant digits given. 

The significant digits of a number are tlie digits from tlie first nonzero digit on tlie left to eitlier (a) the last digit (whetlier it is a nonzero or zero) on tlie right if tliere is a decimal point, or (b) tlie last nonzero digit of the number if tliere is no decimal point. For example ... 

Double precision—Vdilue stored as two words, rather than one, representing a real number, but allowing for approximately double the number of significant digits. 

The number of significant figures is the number of digits shown when a quantity is expressed in exponential notation. 

Case Amount c Subtracted Digits Typed in Number of Significant Digits... 

Notice that a result of this type, in order to be interpretable, must comprise three numbers the mean, the (relative) standard deviation, and the number of measurements that went into the calculation. All calculations are done using the full precision available, and only the final result is rounded to an appropriate precision. The calculator must be able to handle >4 significant digits in the standard deviation. (See file SYS SUITAB.xls.)... 

Two numbers of s significant digits each, when multiplied, require 2 s digits for the result. 

The division of two numbers of s significant digits each can yield results that require nearly any number of digits (only a few if one number is a simple multiple of the other, many if one or both numbers are irrational) usually the number of bytes the computer displays or uses for calculation... 

The programmable calculator or PC that is to be used must be able to work with the number of significant digits required by the algorithm rounding the coefficients can appreciably alter the results of an approximation. 

Round, Column Width) permits the raw data presentation to be adjusted by choosing the number of significant digits to which the numbers are rounded to, see Presentation of Numbers below the column width is automatically adjusted. 

Presentation of Numbers All numbers are presented in the Anglo-American decimal point format, [NNNN.NNN], that is, without commas to separate groups of three digits. A custom-designed procedure displays a number with the preset number of significant digits as long as the chosen number... 

In practice, in numerical calculations with a computer, both rational and imtiooal numbers are represented by a finite number of digits. In both cases, then, approximations are made and die errors introduced in the result depend on the number of significant figures carried by the computer - the machine precision. In die case of irrational numbers such errors cannot be avoided. 

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