Physics
SI Prefixes
SI prefixes are used to denote decimal multiples and submultiples of SI units. They are added to the unit symbol to represent values that are either larger or smaller than the base unit. Common SI prefixes include kilo (k), mega (M), giga (G) for multiples, and milli (m), micro (μ), nano (n) for submultiples. These prefixes make it easier to work with very large or very small measurements.
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eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
Table 1-1 shows the units for the three base quantities—length, mass, and time—that we use in the early chapters of this book. These units were defined to be on a “human scale.” Many SI derived units are defined in terms of these base units. For example, the SI unit for power, called the watt (W), is defined in terms of the base units for mass, length, and time. Thus, as you will see in Chapter 7, 1 watt = 1 W = 1 kg ⋅ m 2 /s 3 , (1-1) where the last collection of unit symbols is read as kilogram-meter squared per second cubed. To express the very large and very small quantities we often run into in physics, we use scientific notation, which employs powers of 10. In this notation, 3 560 000 000 m = 3.56 × 10 9 m (1-2) and 0.000 000 492 s = 4.92 × 10 −7 s. (1-3) Scientific notation on computers sometimes takes on an even briefer look, as in 3.56 E9 and 4.92 E–7, where E stands for “exponent of ten.” It is briefer still on some calculators, where E is replaced with an empty space. As a further convenience when dealing with very large or very small mea- surements, we use the prefixes listed in Table 1-2. As you can see, each prefix represents a certain power of 10, to be used as a multiplication factor. Attaching a prefix to an SI unit has the effect of multiplying by the associated factor. Thus, we can express a particular electric power as 1.27 × 10 9 watts = 1.27 gigawatts = 1.27 GW (1-4) 2 CHAPTER 1 MEASUREMENT Table 1-1 Units for Three SI Base Quantities Quantity Unit Name Unit Symbol Length meter m Time second s Mass kilogram kg Table 1-2 Prefixes for SI Units Factor Prefix a Symbol 10 24 yotta- Y 10 21 zetta- Z 10 18 exa- E 10 15 peta- P 10 12 tera- T 10 9 giga- G 10 6 mega- M 10 3 kilo- k 10 2 hecto- h 10 1 deka- da 10 −1 deci- d 10 −2 centi- c 10 −3 milli- m 10 −6 micro- μ 10 −9 nano- n 10 −12 pico- p 10 −15 femto- f 10 −18 atto- a 10 −21 zepto- z 10 −24 yocto- y a The most frequently used prefixes are shown in bold type.
eBook - ePubQuantities and Units
The International System of Units
- Michael Krystek(Author)
- 2023(Publication Date)
- De Gruyter Oldenbourg(Publisher)
−6 m. However, they do not apply to units that are not SI units. In many countries the use of prefixes is authorized by law.Prefix names are written in capital letters using the font of the surrounding text. They are inseparably attached to the names of the units to which they are prefixed, e. g. millimetres, hectolitres, nanovolts, etc.Prefix symbols, like unit symbols, are always written in upright type (Roman font), regardless of the font used in the surrounding text, without a space between the prefix symbol and the unit symbol. All prefixes for factors greater than 1000 are written in upper case, all others in lower case.Tab. 3.4: Prefix names and prefix symbols for SI units.Factor Name Symbol Factor Name Symbol 1024 yotta Y 0.1 dezi d 1021 zetta Z 10−2 centi c 1018 exa E 10−3 milli m 1015 peta P 10−6 mikro a μ 1012 tera T 10−9 nano n 109 giga G 10−12 piko p 106 mega M 10−15 femto f 103 kilo k 10−18 atto a 102 hecto h 10−21 zepto z 10 deka da 10−24 yokto y aCare must be taken to write the Greek letter μ upright (not italic).The group of characters formed by a unit symbol and a preceding prefix symbol represents a new inseparable unit symbol denoting a multiple or fraction of the corresponding unit. This new unit symbol is therefore treated in the same way as the original unit symbol when calculating with quantity values.Examples:(4.7 μm)2 = (4.7)2 × (10−6 m)2 = 2.209 × 10−11 m215 mg/kg = (15 × 10−3 g)/(103 g) = 1.5 × 10−511.3 g/cm3 = (11.3/10−6 ) × 10−3 kg/m3 = 11 300 kg/m31013.25 hPa = (1013.25 × 102) Pa = 101 325 PaPrefix symbols comprising two or more prefix symbols are not permissible. This rule also applies to two or more prefix names. For the unit of mass, e. g. it is not permissible to write μ
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- 2014(Publication Date)
- Learning Press(Publisher)
SI multiples SI Prefixes are commonly used to measure time less than a second, but rarely for multiples of a second. Instead, the non-SI units minutes, hours, days, Julian years, Julian centuries, and Julian millennia are used. SI multiples for second (s) Submultiples Multiples Value Symbol Name Value Symbol Name 10 −1 s ds decisecond 10 1 s das decasecond 10 −2 s cs centisecond 10 2 s hs hectosecond 10 −3 s ms millisecond 10 3 s ks kilosecond 10 −6 s µs microsecond 10 6 s Ms megasecond 10 −9 s ns nanosecond 10 9 s Gs gigasecond 10 −12 s ps picosecond 10 12 s Ts terasecond 10 −15 s fs femtosecond 10 15 s Ps petasecond 10 −18 s as attosecond 10 18 s Es exasecond 10 −21 s zs zeptosecond 10 21 s Zs zettasecond 10 −24 s ys yoctosecond 10 24 s Ys yottasecond Common prefixes are in bold ____________________ WORLD TECHNOLOGIES ____________________ 3. Kilogram Kilogram A computer-generated image of the International Prototype Kilogram (“IPK”). The IPK is the kilogram. It sits next to an inch-based ruler for scale. The IPK is made of a platinum-iridium alloy and is stored in a vault at the BIPM in Sèvres, France. Like the other prototypes, the edges of the IPK have a four-angle chamfer to minimize wear. Standard: SI base unit Quantity: Mass Symbol: kg Expressed in: 1 kg = Natural units 4.59467(23)×10 7 Planck masses Energy 1.356392733(68)×10 50 hertz 89,875,517,873,681,764 joules (precisely) U.S. customary ≈ 2.204622622 pounds-avoirdupois The kilogram (symbol: kg) is the base unit of mass in the International System of Units ( SI , from the French Le S ystème I nternational d’Unités ), which is the modern standard governing the metric system. The kilogram is defined as being equal to the mass of the International Prototype Kilogram ( IPK ), which is almost exactly equal to the mass of one liter of water. It is the only SI base unit with an SI prefix as part of its name.
eBook - PDFChemistry
The Molecular Nature of Matter
- Neil D. Jespersen, Alison Hyslop(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
The SI solves this problem by forming larger or smaller units by applying decimal multipliers to the base units. Table 1.5 lists the decimal multipliers and the prefixes used to identify them. These were set by the International Bureau of Weights and Measures in 2019. Those listed in red type are the ones most commonly encountered in chemistry. When the name of a unit is preceded by one of these prefixes, the size of the unit is modified by the corresponding decimal multiplier. For instance, the prefix kilo indicates a multiplying factor of 10 3 , or 1000. Therefore, a kilometer is a unit of length equal to NOTE A modified base unit can be conveniently converted to the base unit by removing the prefix and inserting × 10 x . 25.2 pm = 25.2 × 10 −12 m 1.4 Measurement of Physical and Chemical Properties 41 1000 meters. 4 The symbol for kilometer (km) is formed by applying the symbol meaning kilo (k) as a prefix to the symbol for meter (m). Thus 1 km = 1000 m (or 1 km = 10 3 m ). Simi- larly a decimeter (dm) is 1/10th of a meter, so 1 dm = 0.1 m (1 dm = 10 −1 m ). Laboratory Measurements Length, volume, mass, and temperature are the most common measurements made in the laboratory. Length The SI base unit for length, the meter (m), is too large for most laboratory pur- poses. More convenient units are the centimeter (cm) and the millimeter (mm). Using Table 1.5 we see that they are related to the meter as follows. 1 cm = 10 ‒2 m = 0.01 m 1 mm = 10 ‒3 m = 0.001 m TOOLS Units in laboratory measurements 4 In the sciences, powers of 10 are often used to express large and small numbers. The quantity 10 3 means 10 × 10 × 10 = 1000. Similarly, the quantity 6.5 × 10 2 = 6.5 × 10 × 10 = 650. Numbers less than 1 have negative exponents when expressed as powers of 10. Thus, the fraction 1/10 is expressed as 10 −1 , so the quantity 10 −3 means 1 ⁄ 10 × 1 ⁄ 10 × 1 ⁄ 10 = 1 ⁄ 1000. A value of 6.5 × 10 −3 = 6.5 × 1 ⁄ 10 × 1 ⁄ 10 × 1 ⁄ 10 = 0.0065.
eBook - PDFElectrical Principles & Practice NQF2 SB
TVET FIRST
- Jowaheer Consulting and Technologies(Author)
- 2013(Publication Date)
- Macmillan(Publisher)
SI base units As you have learnt, there are different types of SI units of measurement. There are seven SI base units and many derived units. The base units are combined to form derived units. Table 1.1 shows the seven SI base units. ? ? ? Did you know? The SI units were adopted by 36 countries at the 11 th General Conference on Weights and Measures held in France in 1960. Figure 1.2 SI units are used worldwide Words & terms unit of measurement: a defined, physical quantity in terms of which other quantities of the same kind may be expressed as simple multiples of the unit of measurement physical quantity: the property of a phenomenon, body or substance where the property has a magnitude that can be expressed as a number and a reference Module 1 SI Units of measurement 5 Physical quantity Physical quantity symbol SI base unit SI base unit symbol length l metre m mass m kilogram kg time t second s electric current I ampere A temperature T kelvin K luminous intensity I v candela cd amount of a substance n mole mol Table 1.1 The seven SI base units For a measurement to be of value, a unit of a physical quantity must have the same magnitude regardless of where you take the actual measurement. By convention, the units of measurement of the seven base quantities have been defined as explained below. Metre (m) The metre (m) is the base unit of length ( l ). The metre is defined as follows: A metre is the length of the path travelled by light in a vacuum during a time interval of 1 ⁄ 299 792 458 of a second. Table 1.2 shows SI multiples for the metre (m). Submultiples Multiples Value Symbol Name Value Symbol Name 10 −1 m dm decimetre 10 1 m dam decametre 10 −2 m cm centimetre 10 2 m hm hectometre 10 −3 m mm millimetre 10 3 m km kilometre 10 −6 m µm micrometre 10 6 m Mm megametre 10 −9 m nm nanometre 10 9 m Gm gigametre 10 −12 m pm picometre 10 12 m Tm terametre Table 1.2 SI multiples for the metre (m) Note 1.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
Table 1.1.1 shows the units for the three base quantities— length, mass, and time—that we use in the early chapters of this book. These units were defined to be on a “human scale.” Many SI derived units are defined in terms of these base units. For example, the SI unit for power, called the watt (W), is defined in terms of the base units for mass, length, and time. Thus, as you will see in Chapter 7, 1 watt = 1 W = 1 kg ⋅ m 2 /s 3 , (1.1.1) where the last collection of unit symbols is read as kilogram-meter squared per second cubed. To express the very large and very small quantities we often run into in physics, we use scientific notation, which employs powers of 10. In this notation, 3 560 000 000 m = 3.56 × 10 9 m (1.1.2) and 0.000 000 492 s = 4.92 × 10 −7 s. (1.1.3) Scientific notation on computers sometimes takes on an even briefer look, as in 3.56 E9 and 4.92 E–7, where E stands for “exponent of ten.” It is briefer still on some calculators, where E is replaced with an empty space. Table 1.1.1 Units for Three SI Base Quantities Quantity Unit Name Unit Symbol Length meter m Time second s Mass kilogram kg 3 1.1 MEASURING THINGS, INCLUDING LENGTHS As a further convenience when dealing with very large or very small measure- ments, we use the prefixes listed in Table 1.1.2. As you can see, each prefix represents a certain power of 10, to be used as a multiplication factor. Attaching a prefix to an SI unit has the effect of multiplying by the associated factor. Thus, we can express a particular electric power as 1.27 × 10 9 watts = 1.27 gigawatts = 1.27 GW (1.1.4) or a particular time interval as 2.35 × 10 −9 s = 2.35 nanoseconds = 2.35 ns. (1.1.5) Some prefixes, as used in milliliter, centimeter, kilogram, and megabyte, are probably familiar to you. Changing Units We often need to change the units in which a physical quantity is expressed.
eBook - PDFEngineering Technology NQF2 SB
TVET FIRST
- Jowaheer Consulting and Technologies Business Programme Developments(Author)
- 2013(Publication Date)
- Macmillan(Publisher)
All the other SI units are derived from these seven base units. In a decimalised system, all units are related by powers of 10 and are identified by prefixes. This makes the conversion of units easier. For example, it is easy to convert metres to millimetres by simply moving the decimal point – 1,456 metres is 1 456 millimetres. You will learn more about this in Unit 5.2. Did you know? Lord Kelvin, a scientist, said: When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of science. 176 Module 5: SI units of measurement Defining a unit of measurement and physical quantity A unit of measurement is a defined, physical quantity in terms of which other quantities of the same kind may be expressed as simple multiples of the unit of measurement. For example, length is a physical quantity. The SI unit of measurement for length is the metre. The International System of Units defines the metre as follows: A metre is the length of the path travelled by light in a vacuum during a time interval of 1 ⁄ 299 792 458 of a second. Example 1 FIFA specifies the field dimensions of a soccer field as follows: Length: min 90 m max 120 m Width: min 45 m max 90 m Here, FIFA is expressing other quantities of the metre in terms of simple multiples of the metre. So, the length of a soccer field must be a minimum of 90 metres and a maximum of 120 metres. Physical quantity is a physical property of a phenomenon, body or substance that can be quantified by measurement. A more formal definition is given in the International Vocabulary of Metrology , 3rd edition (VIM3), which defines quantity as: the property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference.
eBook - ePub- John Bird(Author)
- 2021(Publication Date)
- Routledge(Publisher)
Chapter 8Units, prefixes and engineering notation
In engineering there are many different quantities to get used to, and hence many units to become familiar with. For example, force is measured in newtons, electric current is measured in amperes and pressure is measured in pascals. Sometimes the units of these quantities are either very large or very small and hence prefixes are used. For example, 1000 pascals may be written as 103 Pa which is written as 1 kPa in prefix form, the k being accepted as a symbol to represent 1000 or 103 . Studying, or working, in an engineering discipline, you very quickly become familiar with the standard units of measurement, the prefixes used and engineering notation. An electronic calculator is extremely helpful with engineering notation.Why it is important to understand:its, prefixes and engineering notationAt the end of this chapter you should be able to:- state the seven SI units
- understand derived units
- recognise common engineering units
- understand common prefixes used in engineering
- express decimal numbers in standard form
- use engineering notation and prefix form with engineering units
8.1. Introduction
Of considerable importance in engineering is a knowledge of units of engineering quantities, the prefixes used with units, and engineering notation. We need to know, for example, that80 kV = 80 ×10 3V , which means 80 000 voltsThis is explained in this chapter.and25 mA =25×10A,− 3which means 0 .025 amperesand50 nF =50×10F,− 9which means 0 .000000050 farads8.2. SI units
The system of units used in engineering and science is the Système Internationale d’Unités (International System of Units
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