Number, defined, significant digits

The mole (abbreviated mol) is the standard chemical unit used to measure the quantity of a substance. A mole is defined as the number of C atoms in exactly 12 g of C. The mole is equal to 6.0221367 X 10 particles. Thus the mole is a number, essentially like a dozen, except very much larger. This number is about the number of grains of sand that would fit into a sphere the size of the Earth. (See Problem 2.154.) This numbCT is known as Avf adro s number. Remember the value of this number to at least three significant digits. 

The uncertainty of a value basically defines the number of significant digits a value should be given. 

The number of significant digits in the answer is determined by the numbers in our measurements, not in defined values like the number of millimeters in a meter. 

The "1" in the conversion factor is defined, or exact, and does not limit the number of significant digits. 

Some numbers are pure numbers and are not subject to the uncertainties of measurement. Such numbers are said to be exact. For example, the number of runs performed in an experiment is an exact number. If you performed three runs, there is no uncertainty as to whether you completed 2.8, 2.97, or 3.1 runs. You completed exactly 3 runs, and the number can be expressed as 3.00... to an infinite number of digits. Defined quantities such as 1000 mL/1 L are also exact numbers and have an infinite number of significant figures. You should learn to recognize exact numbers. 

CAS numbers are identifying numbers allocated to each distinctly definable chemical substance indexed by CAS since 1965 (plus some retrospective allocation of numbers by CAS to compounds from earlier index periods). The numbers have no chemical significance but they provide a label for each substance independent of any system of nomenclature. They are extensively used for exchanging information between individuals and databases. The numbers take the form NNNNNN-NN-R, where the total number of digits is five or more and R is a check digit. 

A counted significant figure is something that cannot be divided into subparts. These are recorded in whole numbers such as 9 chickens, 2 bicycles, or 7 keys. Defined significant digits are exact numbers, but not always whole numbers, like 2.54 centimeters equals one inch. 

Note that the indirect statement of uncertainty in the expression (b) is not very well defined. In both of the above cases, the number of significant digits has been determined so that the uncertainty concerns the last digit in the result. Generally, for estimates of uncertainty, an accuracy in the estimate of uncertainty better than 10 - 20 % is seldom necessary therefore, the uncertainty is given with a maximum of two significant digits. 

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