A In Problems 5 to 15, evaluate the expressions given.
Chapter 8 Units, prefixes and
engineering notation
Why it is important to understand:Units, 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 103Pa, 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. At 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 knowl- edge of units of engineering quantities, the prefixes used with units, and engineering notation.
We need to know, for example, that
80 kV=80×103V,which means 80 000 volts and 25 mA=25×10−3A, which means 0.025 amperes
and 50 nF=50×10−9F, which means 0.000000050 farads
This is explained in this chapter.
8.2
SI units
The system of units used in engineering and science is the Système Internationale d’Unités (International System of Units), usually abbreviated to SI units, and is Understanding Engineering Mathematics. 978-0-415-66284-0, © 2014 John Bird. Published by Taylor & Francis. All rights reserved.
Section
A
Table 8.1Basic SI unitsQuantity Unit Symbol
Length metre m (1 m=100 cm
=1000 mm)
Mass kilogram kg (1 kg=1000 g)
Time second s
Electric current ampere A Thermodynamic temperature kelvin K (K=◦C+273) Luminous intensity candela cd Amount of substance mole mol
based on the metric system. This was introduced in 1960 and has now been adopted by the majority of countries as the official system of measurement.
The basic seven units used in the SI system are listed in Table 8.1 with their symbols.
There are, of course, many units other than these seven. These other units are called derived units and are defined in terms of the standard units listed in the table. For example, speed is measured in metres per second, therefore using two of the standard units, i.e. length and time.
Some derived units are givenspecial names. For exam- ple, force=mass×acceleration has units of kilogram metre per second squared, which uses three of the base units, i.e. kilograms, metres and seconds. The unit of kg m/s2is given the special name of anewton.∗
Table 8.2 contains a list of some quantities and their units that are common in engineering.
8.3
Common prefixes
SI units may be made larger or smaller by using prefixes which denote multiplication or division by a particular amount.
The most common multiples are listed in Table 8.3 on page 64. A knowledge of indices is needed since all of the prefixes are powers of 10 with indices that are a multiple of 3.
Here are some examples of prefixes used with engineer- ing units.
∗Who wasNewton? Go to www.routledge.com/cw/bird
Afrequency of 15 GHzmeans 15×109Hz, which is 15 000 000 000 hertz,
i.e. 15 gigahertz is written as 15 GHz and is equal to 15 thousand million hertz.
(Instead of writing 15 000 000 000 hertz, it is much neater, takes up less space and prevents errors caused by having so many zeros, to write the frequency as 15 GHz.)
A voltage of 40 MV means 40×106V, which is 40 000 000 volts,
i.e. 40 megavolts is written as 40 MV and is equal to 40 million volts. An inductance of 12 mH means 12×10−3H or 12 103H or 12 1000H, which is 0.012 H,
i.e. 12 millihenrys is written as 12 mH and is equal to 12 thousandths of a henry.
Atime of 150 nsmeans 150×10−9s or 150
109s, which is 0.000 000 150 s,
i.e. 150 nanoseconds is written as 150 ns and is equal to 150 thousand millionths of a second.
Aforce of 20 kN means 20×103N, which is 20 000 newtons,
i.e. 20 kilonewtons is written as 20 kN and is equal to 20 thousand newtons.
Acharge of 30μCmeans 30×10−6C or 30
106C, which is 0.000 030 C,
i.e. 30 microcoulombs is written as 30μC and is equal to 30 millionths of a coulomb.
Acapacitance of 45 pFmeans 45×10−12F or 45 1012F, which is 0.000 000 000 045 F,
i.e. 45 picofarads is written as 45 pF and is equal to 45 million millionths of a farad.
In engineering it is important to understand what such quantities as 15 GHz, 40 MV, 12 mH, 150 ns, 20 kN, 30μC and 45 pF mean.
Now try the following Practice Exercise
Practice Exercise 34 SI units and common prefixes (answers on page 1111)
1. State the SI unit of volume. 2. State the SI unit of capacitance. 3. State the SI unit of area. 4. State the SI unit of velocity. 5. State the SI unit of density.
Section
A
Table 8.2 Some quantities and their units that are common in engineering
Quantity Unit Symbol
Length metre m
Area square metre m2
Volume cubic metre m3
Mass kilogram kg
Time second s
Electric current ampere A
Speed, velocity metre per second m/s
Acceleration metre per second squared m/s2
Density kilogram per cubic metre kg/m3
Temperature kelvin or Celsius K or◦C
Angle radian or degree rad or◦
Angular velocity radian per second rad/s
Frequency hertz Hz
Force newton N
Pressure pascal Pa
Energy, work joule J
Power watt W
Charge, quantity of electricity coulomb C
Electric potential volt V
Capacitance farad F
Electrical resistance ohm
Inductance henry H
Moment of force newton metre N m
6. State the SI unit of energy. 7. State the SI unit of charge. 8. State the SI unit of power. 9. State the SI unit of angle.
10. State the SI unit of electric potential. 11. State which quantity has the unit kg. 12. State which quantity has the unit symbol.
13. State which quantity has the unit Hz. 14. State which quantity has the unit m/s2. 15. State which quantity has the unit symbol A. 16. State which quantity has the unit symbol H. 17. State which quantity has the unit symbol m. 18. State which quantity has the unit symbol K. 19. State which quantity has the unit Pa.
Section
A
Table 8.3 Common SI multiplesPrefix Name Meaning
G giga multiply by 109 i.e.×1 000 000 000
M mega multiply by 106 i.e.×1 000 000
k kilo multiply by 103 i.e.×1000
m milli multiply by 10−3 i.e.× 1
103 = 1
1000=0.001
μ micro multiply by 10−6 i.e.× 1
106 = 1
1 000 000=0.000001
n nano multiply by 10−9 i.e.× 1
109 = 1
1 000 000 000=0.000 000 001
p pico multiply by 10−12 i.e.× 1
1012 =
1
1 000 000 000 000=
0.000 000 000 001
20. State which quantity has the unit rad/s. 21. What does the prefix G mean?
22. What is the symbol and meaning of the prefix milli?
23. What does the prefix p mean?
24. What is the symbol and meaning of the prefix mega?
8.4
Standard form
A number written with one digit to the left of the decimal point and multiplied by 10 raised to some power is said to be written instandard form.
For example, 43 645=4.3645×104in standard form and 0.0534=5.34×10−2in standard form
Problem 1. Express in standard form (a) 38.71