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The Measure of Things 4.15 Standing at the kerbside, the eye measures, at the brains command; converging vehicle speed, height of kerb to roadside, speed required to cross safely. Go or stay. Multiple calculations of measure at the speed of light. No margin of error, a mistake could be terminal. In a supermarket aisle reaching for a packet, or scaling a mountain , multiple internal measures, without which, we could not function at the level of complexity required of the human condition. Our internal measures are unique, as we as individuals are. Moreover our scales of measurement must cope with the exigency of gestation to old age. Quite clearly measurement and number are the first requirement of a civilisation, if it is to function as a higher organism within the whole. A standard measure is created and adhered to. In this way we may refer to a �head of state or the �military arm� when speaking of these complex higher organisms of State which are only made possible by number and measure. There are many different systems of measurement in use throughout the world, with each one having its own standard, the standard being a specific measure to which other things are compared. It will be appreciated that conversion tables, although necessary, are time consuming, cumbersome and prone to user error. In the context of chemistry, medicine or pharmacy, an error could have tragic consequences. Teach yourself the Metric System. The rapid global expansion of science and technology meant that a coherent global system of units was not only desirable, but very necessary. From 10 fingers and 10 toes, it is not a great intellectual leap to one of our earliest counting machines, the �Abacus� which still finds widespread use in the West for the teaching of place and number in units of 1 to 10. The Metric System 4.16 A coherent metric system was first proposed in Lyon, France around 1690. Just over 100 years later the system was standardised by the Paris Academy of Sciences, and was finally legalised in 1801. Since that time it has undergone various revisions, which are carried out by the International Bureau of Weights and Measures. We are able to make sense of very large numbers by the use of Powers, Prefix and symbol. For example, a metric billion means 1000 000 000 000 (1 million, million). We may write that number by the use of Power. A billion has 12 zero,s and is written 10^{12} . One million (1000 000) has 6 zero,s and is written 10^{6}. We operate in the same way when dealing with very small numbers, except the decimal point moves to the left and is designated as the negative power and is indicated by a negative sign. E.g. 1 millionth part of (0.000 001) is written 10^{6} Powers of 10. Table 4.16A
Number, Power and Indices 4.17 If a number is raised to the power of 2, it is said to be �squared�, eg., the area of a house or land is 10 square metres, it can be written as 10^{2} or 10 metre^{2} . If a number is raised to the power of 3, it is said to be �cubed� eg, the volume occupied by a house is 50 cubic metres, and written, 50� or 50 metre^{3} Negative Power or Index 4.18 Example 3^{3} means 1 � 3 � 3 � 3, which equals 0.037; Another example, 10^{3} means 1 � 10 � 10 � 10 = 0.001. It may be seen that with negative powers, the decimal point moves to the left of the conversion factor, by the number of places indicated by the index, or power number. Multiplying by Power 4.19 The International System of Units 4.20 The importance of the S.I. System cannot be overstated because we can communicate core concepts of any activity in precision language. For the population at large, and for all practical purposes, we can consider the Metric and S.I. systems as identical. Physical and Base Quantities 4.21 I often say that when you can
measure what you are speaking about, and express it in numbers, Lord Kelvin was a British Physicist, who amongst other things formulated the second law of thermodynamics in 1850. He also introduced an absolute temperature scale, the units of which were named the Kelvin. The S.I. Units can be described as universal currency of concepts, in which inflation or devaluation are not allowed, unless by international agreement. The base unit must accord with whatever is being counted or measured, for instance; give me 100 dollars worth of apples is meaningless, in the context of the number of apples that are purchased. If, however, $100 will buy 50 kilogram of apples, we then know something about the mass of apples, but nothing about the mass of a single apple. The kilogram is the base unit for mass, therefore, the mass of an individual apple would be a submultiple of the kilogram, and would be expressed as �x� number of grams. There are currently 7 base quantities which are defined by the S.I.System. Table 4.21A Base Quantities and Units
If we wish to know the volume of the mass, then it would be necessary to use a different base unit, in this case the metre ^{3 }; the volume would then be expressed as a sub multiple of the metre, i.e. centimetres or millimetres cubed. Such units are known as derived units. Table 4.21B. Selected Derived Units S.I. System.
N.B. A Pascal = Newton /metre ^{3} Conversion Factors 4.22 Table 4.22A
Table 4.22B
Table 4.22C
Table 4.22D
Table 4.22E
Table 4.22F
Table 4.22G
Miscellaneous Factors 4.23 p or pi ,is the 16th letter of the Greek alphabet, and is used as a math symbol that denotes the ratio of the circumference of a circle to its diameter i.e. p = 3.14159. The diameter of a circle is a straight line from edge to edge, passing through the centre. The radius of a circle is half the diameter. The circumference is the distance around the edge of a complete circle. Figure 4.23A r = radius D = diameter C = circumference The Area of a circle. = p r^{2} = 3.14159 x square of radius. Example. Assume the radius of a circle is 25cm, then the calculation is; r^{2} = r x r = 25 x 25 = 625cm therefore, the area of the circle is 3.14159 x 625 = 1963.49cm�. The volume of a cylinder = p ^{2} x height = p x height x r^{2}, in other words, the area of 1 end x height. Example. The height of a drum or cylinder is 100cm, then the calculation is; Area = 1963.49 x 100 = 196349cm^{3}. When measuring area, 2 dimensional space is measured. When measuring volume, 3 dimensional space is measured. Example. The area of a rectangle is length x breadth = area. The volume of a cube is length x breadth x height.
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