Handling Numbers

Having surveyed some of the units used in chemistry, we now turn to techniques for handhng numbers associated with measurements scientific notation and significant figures. 

Chemists often deal with numbers that are either extremely large or extremely small. For example, in 1 g of the element hydrogen there are roughly 

These numbers are cumbersome to handle, and it is easy to make mistakes when using them in arithmetic computations. Consider the following multiplication  

It would be easy for us to miss one zero or add one more zero after the decimal point. Consequently, when working with very large and very small numbers, we use a system called scientific notation. Regardless of their magnitude, all numbers can be 

Note that the decimal point is moved to the left by two places and n = 2. 

---

As usual, Feynman was right. His little particles captures an essential fact about atoms. They are tiny—so tiny that a teaspoon of water contains about 500,000,000,000,000,000,000,000 of them. Handling numbers this big is awkward. Try dividing it by 63, for example. To accommodate the very large numbers encountered in counting atoms and the very small ones needed to measure them, chemists use the scientific notation system. 

Clinical trial data come in two basic forms numeric variables and text variables. Numeric variables are easy for the statistical programmer to handle. Numbers can be analyzed with SAS in a continuous or categorical fashion without much effort. If a numeric variable needs categorization, it is easy enough to categorize the data within SAS. For example, if you had to classify patient age, a simple DATA step such as the following might serve well. 

Thus on plotting log k for reaction of the esters (1) against log K for ionisation of the acids (2) (he actually plotted the -log values so as to have more easily handled numbers) a reasonable straight line resulted (Fig. 13.1) ... 

Note (2) It is more difficult to find K in scientific notation because most calculators cannot handle numbers this big. So, use what you know about exponents to solve for K ... 

The frequency of this sampling is defined in samples per second. Most A/D boards can sample at about 30,000 points/sec, while an HPLC signal requires sampling at no more than 10 points/sec. The other controlling variable is the size of the output digital number. A typical A/D board can only process a number up to 65,000 to process the full range of detector outputs, at least a 12-bit board is required and many boards use a 16-bit data path that allows a word size that can handle numbers up to 1 million. 

A calculator can handle numbers this large (or this small) only if logarithms are used. Taking the base-f 0 logarithms of both denominators gives... 

So far as the tyro is concerned theoretical demonstrations are by no means so convincing as is sometimes supposed. It is as necessary to learn to think in letters and to handle numbers and quantities by their symbols as it is to learn to swim or to ride a bicycle. The inutility of general proofs is an everyday experience to the teacher. The beginner only acquires confidence by reasoning about something which allows him to test whether his results are true or false he is really convinced only after the principle has been verified by actual measurement or by arithmetical illustration. The best of all proofs, said Oliver Heaviside... 

The KWIC indexing philosophy has also been successfully applied to chemical notations, in particular the Wiswesser Line Notation. The ease with which computers can handle numbers has also been exploited in handling structural data. In the various structural registries, notably the CAS Registry System 53,54) each compound is assigned a unique number which can then be used as the label for the compound rather than the full structural record. 

B) Electronvolt, eV, is an old unit physicists have been using it gives simple, small, easy to handle numbers. To convert an energy given in joules to electronvolts you should always think of this relation 1 volt (electric potential) x 1 coulomb (electric charge) = 1 joule ... 

An essential skill in chemistry is the ability to handle numbers, including very large and very small numbers. An example of the former is Avogadro s number, which is discussed in detail in Chapters 2 and 3. Avogadro s number is a way of expressing quantities of entities such as atoms or molecules and is equal to approximately 602 000 000 000 000 000 000 000. A number so large written in this decimal form is very cumbersome to express and very difficult to handle in calculations. It can be expressed much more conveniently in exponential notation. Avogadro s... 

Handling Numbers Scientific notation is used to express large and small numbers, and each number in a measurement must indicate the meaningful digits, called significant figures. 

---