Significant digits/figures

Significant figures Digits that indicate the precision of measurements— digits of a measured number that have uncertainty only in the last digit. 

Use the general rule for significant figures digits reported are significant unless they are zeros whose sole purpose is to position the decimal place. 

There are a few basic numerical and experimental tools with which you must be familiar. Fundamental measurements in analytical chemistry, such as mass and volume, use base SI units, such as the kilogram (kg) and the liter (L). Other units, such as power, are defined in terms of these base units. When reporting measurements, we must be careful to include only those digits that are significant and to maintain the uncertainty implied by these significant figures when transforming measurements into results. 

Table 6-1 lists the experimental quantities, k, T, ct, the transformed variables x, y, and the weights w. (It is necessary, in least-squares calculations, to carry many more digits than are justified by the significant figures in the data at the conclusion, rounding may be carried out as appropriate.) The sums required for the solution of the normal equations are... 

Significant figures provide an indication of the precision with which a quantity is measured or known. The last digit represents, in a quantitative sense, some degree of doubt. For example, a measurement of 8.12 inches implies tliat Uie actual quantity is somewhere between 8.315 and 8.325 inches. This applies to calculated and measured quantihes quantities tliat are known exactly (e.g., pure integers) have an infinite number of significant figures. 

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

This conversion factor is exact the inch is defined to be exactly 2.54 cm. The other factors listed in this column are approximate, quoted to four significant figures. Additional digits are available if needed for vary accurate calculations. For example, the pound is defined to be 453.59237 g. 

Significant figure A meaningful digit in a measured quantity, 9,20-2 lq ambiguity in, 10 in inverse logarithms, 645-647 in logarithms, 645-647 Silicate lattices, 243 Silicon, 242-243 Silver, 540-541 Silver chloride, 433,443-444 Simple cubic cell (SC) A unit cell in which there are atoms at each comer of a cube, 246... 

The digits in a reported measurement are called the significant figures. There are two significant figures (written 2 sf) in 1.2 cm3 and 3 sf in 1.78 g. Section A describes how to find the number of significant figures in a measurement. 

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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