Significant figures defined

Table 1 shows the number of significant figures defined as... 

Quantities are composed of two parts a number (e.g., 5.31) and a unit (e.g., grams). The number must have the proper amount of significant figures, defined as follows ... 

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. 

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. 

Generally, significant figures may be defined as— All digits that are certain plus one which contains some uncertainty are said to be significant figures . 

Figure 5-43. Different significance levels defining the concentration windows for Data Chrom2a.

Numbers from counting (for example, 1 kangaroo, 2 kangaroos, 3 kangaroos) or from defined quantities (say, 60 seconds per 1 minute) are understood to have an unlimited number of significant figures. In other words, these values are completely certain. 

X10 inches. Here, you have to recall that defined quantities (1 foot is defined as 12 inches) have unlimited significant figures. So your calculation is limited only by the number of significant figures in the measurement 345.6 feet. When you multiply 345.6 feet by 12 inches per foot, the feet cancel, leaving units of inches ... 

In conclusion, we wish to comment on the practice of expressing a helical conformation in terms of some commensurable ratio, u /t, and its corresponding repeat distance, c. If the helical conformation is not expressed accurately in terms of simple small numbers, we feel it is preferable to define the conformation in terms of the ratio r = P/s, limited to the number of significant figures. Our point is made tellingly in Table 2 where a change of one standard deviation in r changes u /t from 948/439 to 54/25. Furthermore, there are 82 other possibilities for t <500. 

The two zeros do not define the position of the decimal point and are significant figures. 

Developing the validation protocol is a crucial step in the validation process. It is the culmination of the regulatory and technical accomplishments to this point in the development of the method. The protocol must define which validation parameters are needed and the specific experiments necessary to demonstrate the validity of the analytical method. The protocol must contain all of the acceptance criteria for each of the relevant validation parameters. Additionally, the protocol must define the number of replicates, the reporting format, and the number of significant figures. In short, the validation protocol instructs the analyst on how to validate the analytical method. 

An exact number is a small number that can be reproducibly determined by counting or one that is defined to a particular value. Exact numbers have infinite precision and significant figures. Exact numbers are not obtained using measuring devices. 

It is very important to report the results of analyses in ways that are readily and unambiguously understood. The methods used to determine average values, standard deviations, confidence intervals, uncertainties etc. must be clearly defined. In some application areas, the concept of a reporting limit is useful it is stated that the concentration of the analyte is not less than a particular value. Prudence indicates that this limit should be greater than the limit of detection (see Section 2.3). Use of an appropriate number of significant figures is also critical in reporting results, as this indicates the precision of the measurements. 

Another value that can have an unlimited number of significant figures is a conversion factor. There is no uncertainty in the values that make up this conversion factor, such as I m = 1000 mm, because a millimeter is defined as exactly one-thousandth of a meter. 

Counting numbers and defined constants have an infinite number of significant figures. 

At sea level, the average air pressure is 760 mm Hg when the temperature is 0°C. Air pressure often is reported in a unit called an atmosphere (atm). One atmosphere is equal to 760 mm Hg or 760 torr or 101.3 kilopascals (kPa). Table 13-1 compares different units of pressure. Because the units 1 atm, 760 mm Hg, and 760 torr are defined units, they have as many significant figures as needed when used in calculations. Do the problem-solving LAB to see how the combined pressure of air and water affects divers. 

An inch is defined as exactly 2.54 cm. The length of a table is measured as 505.16 cm. Compute the length of the table in inches. Justify the number of significant figures in the... 

Exact numbers can be considered as having an unlimited number of significant figures. This applies to defined quantities. 

How do defined quantities affect significant figures Any quantity that comes from a deftnition is exact, that is, it is known to an unlimited number of significant figures. In Example 1-3, the quantities 5280 ft, 1 mile, 12 in., and 1 ft all come from definitions, so they do not limit the significant figures in the answer. 

In Chapter 1 you learned that the specific heat of water is 4.18 J/g °C. The molar heat capacity is defined as the specific heat or heat capacity per mole of material. Calculate the molar heat capacity for water. What value(s) limited the number of significant figures in your answer ... 

Define significant figure. Discuss the importance of using the proper number of significant figures in measurements and calculations. 

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