Significant figures precision with

Finally, it is important to note that the precision of quantities is often not arbitrary. Measuring tools have limits on the precision of measurement. Such measures will have a particular number of significant figures. Calculations with measurements may not result in an increase in the number of significant figures. There are two rules to follow to determine the number of significant figures in the result of calculations ... 

The electron affinities of atoms are presented in Figure 8.2 in the form of a Periodic Table. This format will be used to concisely present the data, whereas the complete values will be given in the appendix. The experimental values are given with the proper number of significant figures, or with the random error in the last figure specified in parentheses. Because chemical accuracy and precision are often considered to be 1 meV, the values are only given to within one-tenth... 

The data are as presented from the references and have not been corrected for significant figures/precision his study included a thermodynamic study with different temperatures Not reported or determined... 

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. 

Most measured quantities are not end results in themselves. Instead, they are used to calculate other quantities, often by multiplication or division. The precision of any such derived result is limited by that of the measurements on which it is based. When measured quantities are multiplied or divided, the number of significant figures in the result is the same as that in the quantity with the smallest number of significant figures. 

Atomic masses calculated in this manner, using data obtained with a mass spectrometer can in principle be precise to seven or eight significant figures. The accuracy of tabulated atomic masses is limited mostly by variations in natural abundances. Sulfur is an interesting case in point. It consists largely of two isotopes, fiS and fgS. The abundance of sulfur-34 varies from about 4.18% in sulfur deposits in Texas and Louisiana to 4.34% in volcanic sulfur from Italy. This leads to an uncertainty of 0.006 amu in the atomic mass of sulfur. 

The finai resuit is rounded to two significant figures to match the precision of the current measurement. The amount of goid is significantiy iess than one moie, consistent with the totai charge. 

The isotopic molar masses are precise to five or more significant figures, so we are tempted to express the result with five significant figures. The mass defect is determined by addition and subtraction, however, and two of the isotopic molar masses are known to just three decimal places, so the mass defect is precise to three decimal places, and the... 

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. 

As Hem (1985) notes, a chemical analysis with concentrations reported to two or three, and sometimes four or five, significant figures can be misleadingly authoritative. Analytical accuracy and precision are generally in the range of 2 to 10%, but depend on the technique used, the skill of the analyst, and on whether or not the constituent was present near the detection limit of the analytical method. The third digit in a reported concentration is seldom meaningful, and confidence should not necessarily be placed on the second. 

Balances with few such significant figures to the right of the decimal point (zero to three) are often referred to as ordinary balances or top-loading balances (precision is 100 to 1 mg). A top-loading balance is an electronic ordinary balance with a pan on the top, as shown in Figure 3.3. The electronic... 

In order to effectively utilize the stoichiometry of the reaction involved in a titration, both the titrant and the substance titrated need to be measured exactly. The reason is that one is the known quantity, and the other is the unknown quantity in the stoichiometry calculation. The buret is an accurate (if carefully calibrated) and relatively high-precision device because it is long and narrow. If a meniscus is read in a narrow graduated tube, it can be read with higher precision (more significant figures) than in a wider tube. Thus a buret provides the required precise measurement of the titrant. 

They are very precise because they are within the uncertainty in the last significant figure expressed. It is not known with certainty if the results are accurate, although good precision usually indicates good accuracy. 

Crunching numbers in scientific and exponential notation Telling the difference between accuracy and precision Doing math with significant figures... 

Multiplying or dividing Round the product or quotient so that it has the same number of significant figures as the least-precise measurement — the measurement with the fewest significant figures. 

A temperature measured on one scale can always be converted into a temperature measured on another scale (e.g. Fahrenheit) with mathematical precision (i.e. to as many significant figures as is required—see Section 6.10.1). 

Systematic Errors in Accurate Mass Measurements. 1. Problem Definitions The value of high resolution mass spectrometry is diminished if the mass measurements do not give unambiguous elemental compositions. Accurate mass measurements in FTMS require a precise measurement of ion frequencies and an accurate calibration law for converting ions frequencies to mass. The ion frequencies can be measured to nine significant figures with modern electronics however, the relationship between ion frequencies in the cubic cell and mass still requires further development. 

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