MAKEaBOOK CONVERT NAELOVA9EHQDAF809D423LMNZ69DNQ5I6BL9DSNLNNJJ6R9J3N7V11GAUM5MHWV1U03QHHIW6T9P2YQVSZKI7UXTOFV7O918QN6C75G4TWMKEFHTENSM6JQZ1UGDFPC6LSPRMOAZH6RJIWYKA6BVQRAGPNCGI6A5SSB2HDGFC3EOAS8B6IVPU CONVERT GENERAL INTRODUCTION Measurements of all kinds (time, length, mass, angle, volume etc.) are essential to the development of our civilization. Indeed, it is almost impossible to imagine a world in which none of those were, or could, be measured. Not that is, a world so technologically advanced. Unfortunately, because we were such a spread-out set of communities, many different units of measurement were developed over a long period of time. Then, as trading took place between peoples from different communities, the desirability of using a common system of units became more and more clear, and eventually - in 1960 - such a system (the S I) came into being. The changeover to that system is taking place, but slowly and unevenly, so that there is still a need to be able to convert units expressed in one system to units in another. That is the purpose of this program. It is assumed that users will know something of the units in which they are interested, so little attempt has been made to explain them. A few general notes about the various types of measures are given on pages 7 to 18. Eventually a program like this will have no justification for its existence at all. However, if history is any guide, that day is a long way off! Press - [Page Dn] - to go on. ╔═══════╗ Page ║CONVERT║ [Version 1.0] 1. General introduction ╚═══════╝ 2. Index (this page) Index 3. S I Units to 4. S I Prefixes Manual 5. S I Conventions ▓ -- Further information -- 6. Accuracy of program ▓ ▓ 19. Other works on units -- About the units -- ▓ 20. Significant figures ▓ 21. Significant figures (continued) 7. Area Angle ▓ 22. Naming large numbers 8. Density (+ Relative Density) ▓ 9. Energy ▓ END 10. Fuel consumption ▓ 11. Flow rate (Volume) ▓ ╒════════════════════════════════════╕ 12. Length ▓ │On ALL pages these keys can be used │ 13. Number bases ▓ ├────────────────────────────────────┤ 14. Power ▓ │Q to QUIT this manual completely. │ 15. Pressure (& Stress) ▓ │P to have PRINTOUT of that page. │ 16. Speed ▓ │I to return to this INDEX. │ 17. Temperature ▓ │Page Dn to GO ON a page. │ 18. Volume (Capacity) Weight (Mass)▓ │Page Up to GO BACK a page. │ ▓ ╘════════════════════════════════════╛ Also you can type in a page number = [ ] + ENTER Now? CONVERT S I UNITS (le Système international d'Unités) This system came into being officially in October 1960 and has been adopted by nearly all countries, though rates of usage vary enormously. There are 7 SI base units - Length metre (m) Mass kilogram (kg) Time second (s) Electric current ampere (A) Temperature kelvin (K) Amount of substance mole (mol) Luminous intensity candela (cd) Exact definitions can found in most books dealing with this subject. From the 7 base units all the other units can be derived. Some of these are becquerel coulomb farad henry herz joule newton ohm pascal siemens tesla volt watt weber and several more. It will be noted that many units are named after persons. Usually it is someone who was prominent in the early work done within the field in which the unit is used. A knowledge of the prefixes used in conjunction with the units is important. These are given on the next page. CONVERT PREFIXES to units The S I allows the sizes of units to be made bigger or smaller by the use of appropriate prefixes. For example the electrical unit of a watt is not a big unit even in terms of ordinary household use, so it is generally used in terms of 1000 watts at a time. The prefix for 1000 is kilo- so we speak of kilowatts. For bigger users of electricity it is usual to use megawatts (a million watts) or even gigawatts (1000 million watts). The full range of prefixes with their multiplying factors is - exa 1 000 000 000 000 000 000 E ░ The letters in the ░ peta 1 000 000 000 000 000 P ░ middle are the ░ tera 1 000 000 000 000 T ░ abbreviations to be ░ giga 1 000 000 000 G ░ used. Note capital ░ mega 1 000 000 M ░ and small letters ░ kilo 1 000 k ░ are different! ░ milli m 0.001 micro µ 0.000 001 nano n 0.000 000 001 pico p 0.000 000 000 001 femto f 0.000 000 000 000 001 atto a 0.000 000 000 000 000 001 CONVERT Some S I CONVENTIONS All units when written in full use lower case - watt metre gram second newton ampere kelvin pascal etc. Abbreviations are formed by the first letter of the unit. This is also put in lower case EXCEPT when unit is named after a person when CAPITALS are used. The above units would be abbreviated as - W m g s N A K P etc. Abbreviations for the prefixes are given on the previous page and need care. To see this, look at the difference between M and m ! All prefixes, except one, which make the unit BIGGER use CAPITALS. The exception is k for kilo, to avoid confusion with K for kelvin. All prefixes which make units smaller use lower case letters. An awkward one is that for micro µ. It is a Greek m - and called mu. These rules combine to produce unambiguous units like - mm m² µm Nm kWh GWh kVA pF and many more. Thus - Nm is newton-metres while nm is nano-metres. The S I preferred way of showing a decimal number is to use a comma - 123,65 The allowed alternative use of a point (as used in English-speaking countries) requires only that the point be placed on the line - 123.65 (Not 123∙65) To make large numbers easier to read they may be divided into blocks of three with a 1-digit space between blocks NOT a comma. 51 273 069 482 NOT 51,273,069,482 CONVERT ACCURACY & LIMITS The background arithmetic to the program is done using 15 significant figures. The display is first given to 3 sig.figs. which can be increased to a maximum of 9. [An explanation of sig.figs. is on page 20.] Two exceptions are number bases and temperatures. The question of sig.figs. does not arise with number bases since there are no fractional parts - it works with whole numbers only. Temperatures are given to 2 sig.figs. (which is sufficient in everyday life) but this may be increased to 5 if required. If a value works out to be 0, 1, 10, 100, or 1000 to 9 significant figures then it is shown only as that, with NO decimal places. It must be appreciated that these limits on sig.figs. are arbitrary, decided only by what seemed to be reasonable in the contexts envisaged for users of this program. There is one other constraint upon the accuracy stated above. This is to do with the size of the display. In some cases a value may be so small that all the significant figures asked for cannot be shown. In all conversions limits are put upon what may be entered (and displayed), and this is stated in the bottom panel of the relevant screen. CONVERT AREA This has used a wide variety of units over the centuries, mainly in connection with measuring land. The most commonly used unit for land in English-speaking countries is the acre. The corresponding SI unit is the hectare, which is about 2½ acres. The hectare is actually a hecto-are = 100 ares, and an "are" is 100 square metres, so a hectare is 10 000 square metres. ANGLE The degree must be the only universally recognised unit of measurement that is still the same size as it was when first devised. It is one-360th part of a full-turn, and was defined to be so over 5,000 years ago by the Babylonians. (They used a base-number of 60 quite a lot, which is why it is common in our angle and time systems.) Angle measure is also metricated. The "grade" is defined as one-100th part of a right-angle or quarter-turn, and each grade is divided into 100 parts called centigrades. This system was little used outside of France. The SI unit of angle measure is the radian (about 57.3°) which is mainly used in mathematics and mathematical applications. CONVERT DENSITY For any substance, the density is a measure of the mass of a unit volume of that substance. So it could it be measured in - pounds per cubic foot ounces per gallon tons per cubic yard grams per litre grams per cubic centimetre etc. The SI preferred unit of density is kg/cubic metre. This does lead to some largish numbers - iron is over 7000, wood is about 600 and even cork is over 200. Many workers like to use grams/cubic centimetre which divides all the previous figures by 1000 (to make 7, 0.6 and 0.2 respectively). This unit also has the added merit of simplicity in that gm/cu.cm kg/litre and tonnes/cu.metre are numerically all the same value - a good illustration of the convenience of the metric system. Relative Density (or Specific Gravity) can be closely approximated by looking at the figure given against gm/cu.cm. Technically it must be regarded as an approximation since adjustments for temperature have to be made, but it is close enough for many purposes. Thus if a substance is known to have a density of 76.8 lb/cu.ft. then it could be seen that its Relative Density is about 1.23 (to 3 sig.figs.). This could also be used the other way of course. CONVERT ENERGY The most useful and practical definition of energy is that it is "a measurement of the capacity for doing work" Energy comes from many sources - sunlight, wind, water, coal, oil, gas, etc. and is of various types - thermal, electrical, chemical, nuclear etc. Because there were so many forms of energy, several ways of measuring it were developed over the years, each being the one that seemed most appropriate to the form of energy under consideration. Thus heat was measured by how much of it was needed to warm up some water (the British thermal unit) whilst water-power was measured by finding out how far it would lift up a weight (the foot-pound). It was only during the 19th century that the connection between the two was noticed and later established in a famous experiment by J P Joule (English physicist 1818-1889) when he showed that - 778 foot-pounds was the same as 1 British thermal unit. Once this was understood it became possible, for the first time, to compare the various forms of energy; for example, comparing water-power with coal. It is in his honour that the S.I. standard of energy is the joule (J) which, since it is a rather small unit, is mostly used as kilojoules (kJ). 1 litre of petrol contains about 33 000 kJ 1 kg of coal contains about 27 000 kJ 1 cu.metre of natural gas contains about 38 000 kJ Average sunlight per day reaching the earth is about 700 million kJ CONVERT FUEL CONSUMPTION This a measure which most people use at some time or other even if only in a casual rather than a carefully calculated way. This is in connection with the motor-car, assessing how much it "drinks" as expressed in miles per gallon (m.p.g.). Here there are two units involved, either or both of which can be changed, so we could have miles per litre or kilometres per gallon or kilometres per litre. The converter will deal with all of these. [Note SI interpretation of m.p.g. would be metres per gram!] Fuel consumption can also be stated in another way by saying how much fuel is needed to make the car go a particular distance. This could be put as gallons per mile. However, unless we were describing the fuel consumption of a jumbo-jet, this figure would be rather small. For example, a car doing 35 m.p.g. uses 0.0286 gallons per mile. To make this figure more "friendly" it is usual to state the amount of fuel needed to go a greater distance - say 100 miles. Now 35 m.p.g. becomes 2.86 gallons per 100 miles. In terms of planning fuel requirements for a trip this form is more directly usable. In fact the metric way of expressing fuel consumption has always been in litres per 100 kilometres. All of the forms discussed here are handled by the converter. CONVERT FLOW RATE (Volume) This is a measurement of the speed with which a liquid or gas is moving. The simplest example is probably that of a river, where the rate at which the water moves past some fixed point in a given time can be worked out. The units of time used may be anything from seconds to days. It could be months or years - in the case of a glacier for example - but such long units are not used in most work, and so are not given in this program. Another example of a flow rate often heard quoted is that of an oil-well where the production might be expressed in barrels per hour or per day. The way in which the amount is expressed can be by volume or by mass. Only the volume has been used in this program as being the one most usually met with. The mass for any given volume can be easily worked out if the density of the material is known. CONVERT LENGTH This is probably the most commonly used type of measurement in the world. It is reflected in the number of different units (both by name and by definition) which can be found. Including historical as well as current usage the total count - worldwide - comes to several hundreds. The most well-known historical measure of length is the CUBIT. Research has identified 8 examples of this which range in length from 44 to 64 cm. See what trouble this must cause to anyone wishing to update an old text! Modern industrialised nations are becoming increasingly metricated, though a lot of imperial measures still abound (inches, feet, miles etc.). It is on the conversions between these two systems that this program concentrates. The nautical mile used is the international one of 1852 metres. There are some very large units of length used by astronomers (and writers of science-fiction) which are based on the speed of light which is - 299 792 459 metres per second or 9 460 500 000 000 km/year and this defines 1 light-year = the distance travelled by light in 1 year. There is also the PARSEC which is about 3.26169 light-years. These units are not used in this program. For "imperialists" the light-year is about 5 878 482 000 000 miles. CONVERT NUMBER BASES This particular converter is not concerned with the number of units, as all the others are, but only with the numbers themselves. No attempt will be made to explain what these numbers are, those that have a need to change the base of a number will know why it is they wish to do so! The bases available are 2 to 16 (hexadecimal) and 20. Where necessary, "digits" bigger than 9 are shown by letters. Thus 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 become A, B, C, D, E, F, G, H, I, J No number bigger than 10 million (base 10), or its equivalent value in any other base can be put in. Any attempt to do so will be ignored. CONVERT POWER measures how work is done or energy is used in relation to time. The S I unit of power is the watt (W) which is 1 joule per second. Imagine a bucket of water being raised from a well. The water weighs 9 kg and the well is 40 metres deep. The work to be done (or the energy needed) is 9 x 40 = 360 kg metres (about 3600 joules) and nothing can alter that. What can be varied is the time taken to do that amount of work. It could be done in 1 second (in theory!) or 1 hour, or any other time. To do it in 1 second needs a power of 3600 watts. (3600 J/sec) To do it in 1 hour needs a power of 1 watt. (1 J/sec for 3600 secs!) A litre of petrol contains about 33000 kilojoules. A car travelling at 50 km.p.h. might use 1 litre of petrol in about 10 minutes. This is a power of 55 kW (or about 70 h.p.). Of course, due to the inefficiency of the system, that is NOT the power which is delivered to the wheels which would only be about one-quarter of that (unfortunately!). If the same amount of petrol was burnt in just 1 second - as in an explosion - then it would produce 33000 kW which is over 44000 h.p. CONVERT PRESSURE (& Stress) These are not the same thing in practice, but they both use the same units (force per unit area) and so the same convertor works for either. Quite a variety of units are used to measure pressure. It may be done in - millimetres or inches of mercury atmospheres metres or feet of water millibars pounds per square inch torrs and a few more. The SI preferred unit for pressure is newtons/metre² and called a "pascal", after Blaise Pascal (1623-1662), French mathematician, physicist, theologian. This program deals with a total of 16 different units of pressure, which should cover most needs. CONVERT SPEED The concept of speed is familiar enough to most people. It is a measure of the distance moved in a unit of time. So we can read - ■ a glacier may move at 10 metres/day ■ for swifts there have been speeds recorded of 47 metres/second ■ a snail goes along at about 3 feet/minute ■ light travels at nearly 300000 km/second ■ the land speed record for a car is 740 miles/hour ■ the Atlantic liner United States achieved a speed of 38 knots and many other such esoteric facts. Clearly there are many ways of expressing speed. All of the units exampled above, and several more besides, are dealt with in this program. The S I preferred unit of speed is metres/second. The "knot" used in this program is the S I defined International knot of 1.852 km/hour which is very slightly different from the UK knot of 1.85318 km/hour. CONVERT TEMPERATURES There have been five main temperature scales. Each one is known by the name of the person who invented it. G. D. FAHRENHEIT (1686-1736) a German physicist, in about 1714 proposed the first practical scale that was taken up. He called the freezing-point of water 32° so as to avoid negative temperatures, and the boiling-point 212°. R A F de RÉAUMUR (1683-1757) a French entomologist proposed an 80 degree scale (from 0° to 80°) in 1730. This was used quite a bit but is now obsolete. Anders CELSIUS (1701-1744) a Swedish astronomer, proposed the 100 degree scale (0° to 100°) in 1742. This was widely adopted as the centigrade scale, but as it could be confused with an angular measure (see page 7), in 1948 it officially became the Celsius scale. William Thomson, 1st Lord KELVIN (1824-1907) a Scottish mathematician and physicist worked with J P Joule - about 1862 - to produce an absolute scale of temperature based on laws of heat rather than the freezing-point of water. The Kelvin scale is now the standard one used in all scientific work. Absolute zero which is 0 K is -273.15°C Note that degree (and the ° sign) are not used on the Kelvin scale. William J M RANKINE (1820-1872) A Scottish engineer and scientist promoted the Kelvin scale in its Fahrenheit form where absolute zero is -459.67°F CONVERT VOLUME (& Capacity) The distinction betwen these two terms is blurred for most users. The use of imperial units (cubic feet and gallons) once helped to keep the two ideas apart, but the S I unit of the litre is now commonly used for both. In the past there were many measures of volume (or capacity), nearly every trade had its own, but now litres and cubic metres serve most purposes. One 'odd' relic that is still heard of by many people is the 'barrel' as used for measuring oil. 1 barrel is equivalent to 42 US gallons, this is nearly 160 litres or about 35 UK gallons. Note two different gallons. WEIGHT (Mass) Another pair of words between which most people do not bother to distinguish. In fact 'mass' is probably thought to be a posh way of saying 'weight' by many. There is a difference, but it need not concern the ordinary user. The correct word in most everyday circumstances is 'mass' and this is coming into use more and more. The SI unit of mass is the kilogram. Notice it is defined with a prefix (kilo) already in place. It is the only base unit in the S I for which an actual physical standard is kept and used for comparison. Work is in hand to define it by some reproducible natural phenomena, in the same way that all the other base units are. CONVERT BOOKS The most extensive set of conversion figures held between two covers must be contained in - "Conversion Tables of Units for Science & Engineering" by Ari L Horvath Macmillan Reference Books 1986 ISBN 0-333-40857-8 There are 77 tables ranging from Lengths to Radiation dose equivalents. As an example, the Length table contains the conversion factors for 107 units. There is also a large bibliography (running to four and a half pages) for those who need to look further. For a very comprehensive account of the history of the development of our units try asking your library to get - "The World of Measurements" by H Arthur Klein Allen & Unwin 1975 ISBN 0-04-500024-7 The modern Encyclopaedia Britannica has many references to this topic, but extensive use needs to be made of the index to find them all. It also has a wide selection of weights and measures from countries around the world and the appropriate conversion factors; in this respect it offers more than the book by Horvath mentioned at the top. CONVERT SIGNIFICANT FIGURES The idea of significant figures is important to all those who have to work with numbers, especially with regard to seeing that they are not invested with an importance that is not warranted. The MOST significant figure in any number is the first digit on the left which is NOT a zero. In each of these examples it is marked with a * beneath. 239 38125 707100 0.1605 0.0000234 310.427 0.0074000 * * * * * * * Starting with the most significant, ALL digits (including zeroes) are now counted until either the end of the number is reached, or until only zeroes are left - these are not counted (they may be later - see below). In the above examples the number of significant figures in each is - 3 5 4 4 3 6 2 That is a broad outline, which works well most times. However cases can be complicated by zeroes. It depends where they come. First, if they appear WHEN NOT NECESSARY then they should be considered as significant. Thus in 0.04600 the last two zeroes do nothing for the value of the number, but they do signal that (whatever it is the number is about) has been measured to an accuracy of 4 sig. figs. - the last two happened to be zero. Put another way, 0.04600 implies a greater accuracy than 0.046 -continued- CONVERT SIG FIGS (or s.f.) -continued- Care must be exercised. It is not merely a matter of adding noughts. They should be put there only if it is known the value is that. Thus measuring a line as 23.5cm and calling it 23.5000 has not made the measurement any more accurate. Zeroes which appear BETWEEN non-zeroes (as in 62.07) must be significant since we can see that the measurement has gone beyond that place of accuracy. The difficulty comes with zeroes that are necessary to the size of the number like 17400 - the zeroes are needed else it becomes 174. Now, unless we know more about the number we cannot say whether it is accurate to 3, 4 or 5 s.f. Suppose it had been an estimate of the size of a crowd of people. Then it is reasonable to think that it could not be done closer than in hundreds, in which case 17400 is accurate to 3 s.f. However, suppose it was a reading taken from a counter, of objects coming from a machine. In that case the number could be exact and accurate to 5 s.f. Or it might be that the counter was not quite up to the job and might be a few in error. Now we have a number accurate to 4 s.f. The message of this is clear. If the number itself does not bear evidence of its accuracy then it should carry a statement of what the accuracy is. Thus 1730(to 3 s.f.) 8604 910(to 3 s.f.) 3600(to 2 s.f.) 4000(to 3 s.f.) CONVERT NAMES of Large Numbers This relates to the names given to numbers over a million. A million is known everywhere as 1000 x 1000 = 1 000 000, but after that there are two systems in use. Originally the idea was that when two millions were multiplied together this would make a bi-million or billion and this would be extended to make tri-millions (trillions) and so on. It was the French who later decided that it would be more logical to go up in steps of a thousand each time so a billion was a thousand x a million. This was taken up by America also and is now the more generally used meaning in the world. (When you meet a billionaire, check on her nationality - she might not be worth as much as you thought!) The variation is shown in this table - UK name USA name figures thousand thousand 1 000 million million 1 000 000 thousand million billion 1 000 000 000 billion trillion 1 000 000 000 000 thousand billion quadrillion 1 000 000 000 000 000 trillion quintillion 1 000 000 000 000 000 000 thousand trillion sextillion 1 000 000 000 000 000 000 000 quadrillion septillion 1 000 000 000 000 000 000 000 000 These words are generally used in contexts where effect matters more than accuracy. If size is important then Scientific Notation is used.
