Decimal system

Much of modem life revolves around the use of the decimal system of numbers, although for many purposes it is far from ideal. This system (dec = ten) takes 10 as the basic unit of operation, and we say that we are working to base 10. However, the base 10 is not the only one possible the previous British and many other countries coinage was founded on a base of 12. The meaning of a base for purposes of calculation is illustrated in Figure 42.1. 

Note The sequence of columns in binary runs 1,2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096 and so on, each column being two times greater than the previous one. Compare this with the decimal system where each column is 10 times greater than the previous one. 

SI is a decimal system. Fractions have been eliminated, and multiples and submultiples are formed by a system of prefixes ranging from yotta, for 10 , to yocto, for 10 . Calculations, therefore, are greatiy simplified. 

An example of the first route is given in the preparation of nylon 66, which is made by reaction of hexamethylenediamine with adipie acid. The first 6 indicates the number of carbon atoms in the diamine and the second the number of carbon atoms in the acid. Thus, as a further example, nylon 6.10 is made by reacting hexamethylenediamine with sebacic acid (HOOC (CH2)s"COOH). (In this context the numbers 10,11 and 12 are considered as single numbers the need to use two digits results simply from the limitations of the decimal system.)... 

The metric system uses decimals (or the decimal system). In the metric system, the gram is the unit of weight, the liter the unit of volume, and the meter the unit of lengtii. 

The measurement system that you will most likely encounter is the SI (Metric) system. Each quantity (such as mass and volume) has a base unit and a prefix that modifies the base unit. The prefixes are the same for all quantities and are based on a decimal system. Below are some basic SI units we will introduce others in later chapters ... 

The decimal system is a way to name numbers based on the powers of 10. The numbers to the right of the decimal point are fractional equivalents with denominators that are powers of ten. 

Our number system is the decimal system, where digits are based on the powers of ten. It is natural to want to compare numbers to a common baseline, like one hundred, which is 102. Ratios that are comparisons of a part to a whole are percents when the whole is one hundred. The symbol for percent is % 74% means 74 out of every one hundred. As an example, if two out of every five people live in a city, to find the percent you can use a proportion j = jq(). Cross-multiply to get 5 xp = 2 x 100, or 5 xp = 200. Divide 200 by five to get p = 40. So it is true that 40% of the people five in cities. A ratio such as 2 to 5 is perhaps more clear when expressed as 40%. 

Digital computers use either a decimal or binary system of notations (Ref 3, p 78). The "binary system is a number system which uses two symbols (usually denoted by "0 and "1 ) and has two as its base, just as the "decimal system uses ten symbols (0, 1, 2,. .. 9) and the base ten (Ref 3, p38). Digital computers are also called "discrete , because they recognize only discrete values, 0, 1, 2 etc (Ref 1, p 45)... 

Sections and sub-sections are numbered using a decimal system. Thus, 7.4.1 is the first sub-section of section 4 of Chapter 7 A3.5.2 is the second sub-section of section 5 of Annex 3. Section numbers, rather than page numbers, are used to cross-reference material in other parts of the Workbook. Figures and Tables are numbered consecutively within each chapter, e.g. Figure A2.1 is the first figure in Annex 2. Equations are also numbered consecutively within each Chapter, with the equation number appearing in brackets at the end of the equation. 

One major advantage of the metric system is that it uses a decimal system, which means all units are related to smaller or larger units by a factor of 10. Some of the more commonly used prefixes along with their decimal equivalents are shown in Table 1.2. From this table, you can see that 1 kilometer is equal to 1000 meters, where the prefix kilo- indicates 1000. Likewise, 1 millimeter is equal to 0.001 meter, where the prefix milli- indicates Xooo- You need not memorize this table, but you will find it a useful reference when you come across these prefixes in your course of study. 

CELSIUS. ANDER (1701-1744). Celsius was a Swedish astronomer, mathematician, and physicist. He is best known for his development of a temperature scale based on the decimal system with fixed points separated by one hundred degrees. He proposed all scientific measurements of temperature should be based on the boiling point and the freezing point of water. 

The dilution and mechanical agitation can be done by hand or by a machine. Manual preparation cannot be uniform in strength every time a vial is shaken. Machine is needed for the preparation of higher potencies like CM (diluted one hundred thousand times) and MM (diluted one million times). Hahnemann followed the duodecimal system, which was in vogue in his time, in choosing the potency numbers as 6, 12, 24 etc. Higher potencies like 200, 1M, CM, introduced later are based on the metric or decimal system in units. Besides decimal and centesimal series, based on serial dilution of 1 10 and 1 100, respectively, there exists the millesimal series which is based on the serial dilution of 1 1000 and is denoted with the suffix m (Cook, 1988). 

Hexadecimal to decimal conversion. The system of number conversion from hexadecimal to decimal system is same as from binary to decimal and octal to decimal. The difference is only of their base value because binary number system has its base value as 2, octal has 8 and hexadecimal has 16. This can be understood by the following problem. 

You probably learned how to count in kindergarten, or maybe even earlier than that. Counting to ten is easy now 1,2, 3,4,5,6, 7, 8,9,10. But did you ever think about what those numbers mean We count using the decimal system. We have ten symbols that we use to write numbers. It s easy to overlook the first number 0. 

A DECIMAL IS a number that is written using one or more of ten symbols. The ten decimal symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These ten symbols can be used to write any number in the decimal system, such as 17 or 323,119. The prefix dec- means ten, which is why the decimal system is also called a base-ten system. Each digit in a decimal number is equal to that digit multiplied by a power of ten. 

THE PLACE VALUE system uses a number system, such as the decimal system, and the position (or place) of each digit in a number to determine what value each digit in the number is worth. 

The metric system is a decimal system, based on powers of 10. Table 2.5 is a list of the prefixes for the various powers of 10. Between scientific notation and the prefixes shown below, it is very simple to identify, name, read, and understand 36 decades of power of any given base or derived unit. 

The decimal system is a very popular outlining system it is easy to use and can be set up automatically in most current word processing software applications. This author strongly advises against going beyond three or four levels in the decimal system, because it is difficult to figure out by then which level you are reading. For example, is section 3.1.2.1.2.1.1.1 on the same level as... 

There are two main systems used by libraries to classify books the Dewey Decimal system and the Library of Congress system. Libraries differ in the way they employ these systems, especially by adding further numbers and letters after the standard classification marks to signify, say, shelving position or edition number. Enquire at your library for a full explanation of local usage. 

The base 10 or decimal system has now spread throughout the world and is the most commonly used numeration system today. The digits to the left and right of the decimal point are named according to their distance from the decimal. The first ten numbers, in their order of distance from the left of the decimal point are ... 

Place value systems are important because they make common arithmetic functions much more efficient. If people are to manipulate spatial symbols readily, they need a method that is simple, consistent, and symmetrical so that numbers can be lined up visually and quickly grouped at a glance according to their value. Without the place values of the decimal system, simple arithmetic functions of addition, subtraction, multiplication, and division are enormously difficult because they are intimidating, time-consuming, overly complicated, and prone to error. 

Place-value—The location of a number relative to others in a sequence. In the decimal system the number 3 in the series 2,300 occupies the hundreds place. 

In the binary system, each place from right to left is valued at 2 times the place to its right. Thus the first place can be zero or one, the second place to the left is valued at two, the third place to the left is valued at four, the fourth place to the left is valued at eight, and so on. The following list indicates the binary values of the first ten numbers of a decimal system ... 

Time The SI base unit for time is the second (s). The frequency of microwave radiation given off by a cesium-133 atom is the physical standard used to establish the length of a second. Cesium clocks are more reliable than the clocks and stopwatches that you use to measure time. For ordinary tasks, a second is a short amount of time. Many chemical reactions take place in less than a second. To better describe the range of possible measurements, scientists add prefixes to the base units. This task is made easier because the metric system is a decimal system. The prefixes in Table 2-2 are based on multiples, or factors, of ten. These prefixes can be used with all SI units. In Section 2.2, you will learn to express quantities such as 0.000 000 015 s in scientific notation, which also is based on multiples of ten. 

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