Definition of Measurement Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc. , to a unit of measurement, such as the meter, second or degree Celsius. The science of measurement is called metrology. The English word measurement originates from the Latin mensura and the verb metiri through the Middle French mesure. Reference: http://en. wikipedia. org/wiki/Measurement Measurement Quantities *Basic Fundamental
Quantity name/s| (Common) Quantity symbol/s| SI unit name| SI unit symbol| Dimension symbol| Length, width, height, depth| a, b, c, d, h, l, r, s, w, x, y, z| metre| m| [L]| Time| t| second| s| [T]| Mass| m| kilogram| kg| [M]| Temperature| T, ? | kelvin| K| [? ]| Amount of substance, number of moles| n| mole| mol| [N]| Electric current| i, I| ampere| A| [I]| Luminous intensity| Iv| candela| Cd| [J]| Plane angle| ? , ? , ? , ? , ? , ? | radian| rad| dimensionless| Solid angle| ? , ? | steradian| sr| dimensionless| Derived Quantities Space Common) Quantity name/s| (Common) Quantity symbol| SI unit| Dimension| (Spatial) position (vector)| r, R, a, d| m| [L]| Angular position, angle of rotation (can be treated as vector or scalar)| ? , ? | rad| dimensionless| Area, cross-section| A, S, ? | m2| [L]2| Vector area (Magnitude of surface area, directed normal totangential plane of surface)| | m2| [L]2| Volume| ? , V| m3| [L]3| Quantity| Typical symbols| Definition| Meaning, usage| Dimension| Quantity| q| q| Amount of a property| [q]| Rate of change of quantity, Time derivative| | | Rate of change of property with respect to time| [q] [T]? 1| Quantity spatial density| ? volume density (n = 3), ? = surface density (n = 2), ? = linear density (n = 1)No common symbol for n-space density, here ? n is used. | | Amount of property per unit n-space(length, area, volume or higher dimensions)| [q][L]-n| Specific quantity| qm| | Amount of property per unit mass| [q][L]-n| Molar quantity| qn| | Amount of property per mole of substance| [q][L]-n| Quantity gradient (if q is a scalar field. | | | Rate of change of property with respect to position| [q] [L]? 1| Spectral quantity (for EM waves)| qv, q? , q? | Two definitions are used, for frequency and wavelength: | Amount of property per unit wavelength or frequency. [q][L]? 1 (q? )[q][T] (q? )| Flux, flow (synonymous)| ? F, F| Two definitions are used;Transport mechanics, nuclear physics/particle physics: Vector field: | Flow of a property though a cross-section/surface boundary. | [q] [T]? 1 [L]? 2, [F] [L]2| Flux density| F| | Flow of a property though a cross-section/surface boundary per unit cross-section/surface area| [F]| Current| i, I| | Rate of flow of property through a crosssection/ surface boundary| [q] [T]? 1| Current density (sometimes called flux density in transport mechanics)| j, J| | Rate of flow of property per unit cross-section/surface area| [q] [T]? 1 [L]? | Reference: http://en. wikipedia. org/wiki/Physical_quantity#General_derived_quantities http://en. wikipedia. org/wiki/Physical_quantity#Base_quantities System of Units Unit name| Unit symbol| Quantity| Definition (Incomplete)| Dimension symbol| metre| m| length| * Original (1793): 1? 10000000 of the meridian through Paris between the North Pole and the EquatorFG * Current (1983): The distance travelled by light in vacuum in 1? 299792458 of a second| L| kilogram[note 1]| kg| mass| * Original (1793): The grave was defined as being the weight [mass] of one cubic decimetre of pure water at its freezing point.
FG * Current (1889): The mass of the International Prototype Kilogram| M| second| s| time| * Original (Medieval): 1? 86400 of a day * Current (1967): The duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom| T| ampere| A| electric current| * Original (1881): A tenth of the electromagnetic CGS unit of current. [The [CGS] emu unit of current is that current, flowing in an arc 1 cm long of a circle 1 cm in radius creates a field of one oersted at the centre. 37]]. IEC * Current (1946): The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per metre of length| I| kelvin| K| thermodynamic temperature| * Original (1743): The centigrade scale is obtained by assigning 0° to the freezing point of water and 100° to the boiling point of water. * Current (1967): The fraction 1/273. 16 of the thermodynamic temperature of the triple point of water| ? mole| mol| amount of substance| * Original (1900): The molecular weight of a substance in mass grams. ICAW * Current (1967): The amount of substance of a system which contains as many elementary entities as there are atoms in 0. 012 kilogram of carbon 12. [note 2]| N| candela| cd| luminous intensity| * Original (1946):The value of the new candle is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per square centimetre * Current (1979): The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 ? 012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. | J| Reference: http://en. wikipedia. org/wiki/International_System_of_Units Scientific Notation Scientific notation (more commonly known as standard form) is a way of writing numbers that are too big or too small to be conveniently written in decimal form. Scientific notation has a number of useful properties and is commonly used in calculators and by scientists, mathematicians and engineers.
In scientific notation all numbers are written in the form of (a times ten raised to the power of b), where the exponent b is an integer, and the coefficient a is any real number (however, see normalized notation below), called the significand or mantissa. The term “mantissa” may cause confusion, however, because it can also refer to the fractional part of the common logarithm. If the number is negative then a minus sign precedes a (as in ordinary decimal notation). ————————————————-
Converting numbers Converting a number in these cases means to either convert the number into scientific notation form, convert it back into decimal form or to change the exponent part of the equation. None of these alter the actual number, only how it’s expressed. Decimal to scientific First, move the decimal separator point the required amount, n, to make the number’s value within a desired range, between 1 and 10 for normalized notation. If the decimal was moved to the left, append x 10n; to the right, x 10-n.
To represent the number 1,230,400 in normalized scientific notation, the decimal separator would be moved 6 digits to the left and x 106 appended, resulting in1. 2304? 106. The number -0. 004 0321 would have its decimal separator shifted 3 digits to the right instead of the left and yield ? 4. 0321? 10? 3 as a result. Scientific to decimal Converting a number from scientific notation to decimal notation, first remove the x 10n on the end, then shift the decimal separator n digits to the right (positive n) or left (negative n). The number1. 2304? 06 would have its decimal separator shifted 6 digits to the right and become 1 230 400, while ? 4. 0321? 10? 3 would have its decimal separator moved 3 digits to the left and be-0. 0040321. Exponential Conversion between different scientific notation representations of the same number with different exponential values is achieved by performing opposite operations of multiplication or division by a power of ten on the significand and an subtraction or addition of one on the exponent part. The decimal separator in the significand is shifted x places to the left (or right) and 1x is added to (subtracted from) the exponent, as shown below. . 234? 103 = 12. 34? 102 = 123. 4? 101 = 1234 Significant Figures The significant figures (also known as significant digits, and often shortened to sig figs) of a number are those digits that carry meaning contributing to its precision. This includes all digitsexcept: * leading and trailing zeros which are merely placeholders to indicate the scale of the number. * spurious digits introduced, for example, by calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports.
Inaccuracy of a measuring device does not affect the number of significant figures in a measurement made using that device, although it does affect the accuracy. A measurement made using a plastic ruler that has been left out in the sun or a beaker that unbeknownst to the technician has a few glass beads at the bottom has the same number of significant figures as a significantly different measurement of the same physical object made using an unaltered ruler or beaker. The number of significant figures reflects the device’s precision, but not its accuracy.
The basic concept of significant figures is often used in connection with rounding. Rounding to significant figures is a more general-purpose technique than rounding to n decimal places, since it handles numbers of different scales in a uniform way. For example, the population of a city might only be known to the nearest thousand and be stated as 52,000, while the population of a country might only be known to the nearest million and be stated as 52,000,000. The former might be in error by hundreds, and the latter might be in error by hundreds of thousands, but both have two significant figures (5 and 2).
This reflects the fact that the significance of the error (its likely size relative to the size of the quantity being measured) is the same in both cases. Computer representations of floating point numbers typically use a form of rounding to significant figures, but with binary numbers. The number of correct significant figures is closely related to the notion of relative error (which has the advantage of being a more accurate measure of precision, and is independent of the radix of the number system used).
The term “significant figures” can also refer to a crude form of error representation based around significant-digit rounding; for this use, see significance arithmetic. The rules for identifying significant figures when writing or interpreting numbers are as follows: * All non-zero digits are considered significant. For example, 91 has two significant figures (9 and 1), while 123. 45 has five significant figures (1, 2, 3, 4 and 5). * Zeros appearing anywhere between two non-zero digits are significant. Example: 101. 12 has five significant figures: 1, 0, 1, 1 and 2. Leading zeros are not significant. For example, 0. 00052 has two significant figures: 5 and 2. * Trailing zeros in a number containing a decimal point are significant. For example, 12. 2300 has six significant figures: 1, 2, 2, 3, 0 and 0. The number 0. 000122300 still has only six significant figures (the zeros before the 1 are not significant). In addition, 120. 00 has five significant figures since it has three trailing zeros. This convention clarifies the precision of such numbers; for example, if a measurement precise to four decimal places (0. 001) is given as 12. 23 then it might be understood that only two decimal places of precision are available. Stating the result as 12. 2300 makes clear that it is precise to four decimal places (in this case, six significant figures). * The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if a number like 1300 is precise to the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundred due to rounding or uncertainty.
Various conventions exist to address this issue: * A bar may be placed over the last significant figure; any trailing zeros following this are insignificant. For example, 1300 has three significant figures (and hence indicates that the number is precise to the nearest ten). * The last significant figure of a number may be underlined; for example, “2000” has two significant figures. * A decimal point may be placed after the number; for example “100. ” indicates specifically that three significant figures are meant. * In the combination of a number and a unit of measurement the ambiguity can be voided by choosing a suitable unit prefix. For example, the number of significant figures in a mass specified as 1300 g is ambiguous, while in a mass of 13 h? g or 1. 3 kg it is not. Rounding Off Numbers Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing ? 23. 4476 with ? 23. 45, or the fraction 312/937 with 1/3, or the expression v2 with 1. 414. Rounding is often done on purpose to obtain a value that is easier to write and handle than the original.
It may be done also to indicate the accuracy of a computed number; for example, a quantity that was computed as 123,456 but is known to be accurate only to within a few hundred units is better stated as “about 123,500. ” On the other hand, rounding introduces some round-off error in the result. Rounding is almost unavoidable in many computations — especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating point representation with a fixed number of significant digits.
In a sequence of calculations, these rounding errors generally accumulate, and in certain ill-conditioned cases they may make the result meaningless. Accurate rounding of transcendental mathematical functions is difficult because the number of extra digits that need to be calculated to resolve whether to round up or down cannot be known in advance. This problem is known as “the table-maker’s dilemma”. Rounding has many similarities to the quantization that occurs when physical quantities must be encoded by numbers or digital signals. Typical rounding problems are pproximating an irrational number by a fraction, e. g. , ? by 22/7; approximating a fraction with periodic decimal expansion by a finite decimal fraction, e. g. , 5/3 by 1. 6667; replacing a rational number by a fraction with smaller numerator and denominator, e. g. , 3122/9417 by 1/3; replacing a fractional decimal number by one with fewer digits, e. g. , 2. 1784 dollars by 2. 18 dollars; replacing a decimal integer by an integer with more trailing zeros, e. g. , 23,217 people by 23,200 people; or, in general, replacing a value by a multiple of a specified amount, e. . , 27. 2 seconds by 30 seconds (a multiple of 15). Conversion of Units Process The process of conversion depends on the specific situation and the intended purpose. This may be governed by regulation, contract, Technical specifications or other published standards. Engineering judgment may include such factors as: * The precision and accuracy of measurement and the associated uncertainty of measurement * The statistical confidence interval or tolerance interval of the initial measurement * The number of significant figures of the measurement The intended use of the measurement including the engineering tolerances Some conversions from one system of units to another need to be exact, without increasing or decreasing the precision of the first measurement. This is sometimes called soft conversion. It does not involve changing the physical configuration of the item being measured. By contrast, a hard conversion or an adaptive conversion may not be exactly equivalent. It changes the measurement to convenient and workable numbers and units in the new system. It sometimes involves a slightly different configuration, or size substitution, of the item.
Nominal values are sometimes allowed and used. Multiplication factors Conversion between units in the metric system can be discerned by their prefixes (for example, 1 kilogram = 1000 grams, 1 milligram = 0. 001 grams) and are thus not listed in this article. Exceptions are made if the unit is commonly known by another name (for example, 1 micron = 10? 6 metre). Table ordering Within each table, the units are listed alphabetically, and the SI units (base or derived) are highlighted. ————————————————- Tables of conversion factors
This article gives lists of conversion factors for each of a number of physical quantities, which are listed in the index. For each physical quantity, a number of different units (some only of historical interest) are shown and expressed in terms of the corresponding SI unit. Legend| Symbol| Definition| ?| exactly equal to| ?| approximately equal to| digits| indicates that digits repeat infinitely (e. g. 8. 294369 corresponds to 8. 294369369369369…)| (H)| of chiefly historical interest| ASSIGNMENT IN PHYSICS I-LEC Submitted by: Balagtas, Glen Paulo R. BS Marine Transportation-I Submitted to: Mrs. Elizabeth Gabriel Professor in Physics-Lec