E1 02 Measurement & Scale V6

8/8/2019 E1 02 Measurement & Scale V6

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Nick Brackenbury [email protected] Electronics Notes January 2005 Page 1

LIST OF CONTENTS Section Contents Page Number

1 Summary and Objectives 2

2 Numerals and Numbers 3

3 Significant Places 3

4 Fraction Notation 4

5 Decimal Notation 5

6 Extended Fraction and Decimal Numbers 6

7 Percentage 6

8 Component Tolerance 79 Scientific Notation and the Base of 10 8

10 Scientific Notation and Extended Decimals 9

11 Multiplying and Dividing using Scientific Notation 10

12 Engineering Notation 11

13 Notation Summary & Comparison Table 12

14 Introduction to SI Units 13

15 SI Base and Extended Units of Measurement 14

16 SI Derived Units of Measurement 1517 Table of Electrical Units 16

18 Examples of Scale with SI Units 17

19 Note on Calculator Use 17

20 Note on Computer Use 17

21 Calculation Short Cuts 18 V6


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This Section is to develop an understanding of Mathematical Scale and Units of Measurement. It also covers the associated written notations to ensure correctexpression of measurements verbally, in writing and in arithmetic calculations.

This unit covers revision of basic arithmetic and maths skills that may not have beenused by a student for several years. These skills are necessary in engineeringpractice in measurements and calculations on mechanical, electrical and electronicdesigns. This is essential basic maths for City & Guilds and Edexcel BTECs.

Maths and electronics are inseparable. Calculations and measurements are involvedin every electronic project. Understanding these basic maths procedures and units of measurement origins will make electronic calculations and instrument measurementsmuch easier and more enjoyable.

Mathematical notation is the way in which numbers are written, spoken and used incalculations. A number can be written, spoken or used in a number of different ways.

Each of the notations, as the different ways of expressing numbers are called, has aspecific use. It is important to select the correct notation for each use type.

Design and measurement are two important activities of Engineers. Both require agood understanding and feel for scale and size. Practical experience in conjunctionwith competent handling of numbers will make most aspects of engineering mucheasier to grasp.

This Numbers, Scale, Notation & Units of Measurement module is intended to be readand referred to regularly throughout the year.

There are seven Base Units of measurement - length, weight, time, current, light,temperature and matter. There are two Extended Units of measurement - 2D angleand 3D angle.All other Units of Measurement such as velocity, density and Volts are derived fromthese Base and Extended Units. A table is provided of many mechanical andelectrical derived units of measurement such as acceleration, power, electric chargeand magnetic flux.


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2 N UMERALS AND NUMBERS

An integer is a whole number from 1 to infinity ().

Our numerals 0 to 9 originate from Arabic mathematics, which inturn came from India. There are ten such numerals which weuse to count to the base of 10 .

The ten numerals being 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

It is widely accepted that we have ten numerals, and count tothe base of 10, because we have 10 fingers and thumbs, andthese were our original counting machine.

Counting to the base of 10, number examples are:

17 which is 7+10528 which is 8+20+500

3940 which is 0+40+900+3000

When we say 7, for example, we are saying seven. In English language, we write seven.

Notation is the way we refer to number presentation:

7 is called the numeral 7 seven is the English spoken and written word for 7

All of the above numbers are whole numbers greater than zerocalled integers. Examples of valid integers are:

1234 +98765

1,234 +98,765-1234 - 98,765

We sometimes use a comma , as a marker guide every threedigits starting from the right and counting every three digits tothe left. The , is used to guide the eye; and has nomathematical relevance.

3 S IGNIFICANT P LACES

The first digit on the right is called the units digit. It is also referred toas the least significant digit, being the one that represents thesmallest numerical value.

The second digit from the right is called the tens digit. In the case of the example below it is also referred to as the third most significantdigit.

The third digit from the right is called the hundreds digit. In the caseof the example below it is also referred to as the second mostsignificant digit.

The fourth digit from the right is called the thousands digit. In thecase of the example below it is also referred to as the most

significant digit. It is the most significant digit in this examplebecause, being 6,000, it is the largest part of the number. Thenumber is made up from 6,000 + 300 + 20 + 9 = 6,329

Tensdigit

Unitsdigit

Hundredsdigit

Most & firstSignificant digit

6,329

Thousandsdigit

Secondsignificant

digit

Least & fourthsignificant digit

Thirdsignificant

digit


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Numbers, or values, that are not whole or integer can beexpressed as:

fractions or decimals

Fractions derive from use in verbal conversation, and tend to bepopular in expressions using the more simple fractions such as:

English spoken & written Fractionone eighth one quarter one third three eighths one half five eighths

two thirds three quarters seven eighths

Similar to the whole number integer presentation, fractions can bewritten in numeric form or English language form.

More complex fractions become difficult to express verbally. Theyare also increasingly difficult to use in calculations.

For example - four-hundred-and-seventy-nine six-hundred-and-thirty-thirds (489/633) is cumbersome to say. In fact, fractions are

quite unusable in this form. The top number and bottom number of a fraction are referred to as:489 is numerator = 163633 is denominator 211

The value of a fraction is unchanged if we multiply or divide bothits numerator and denominator by the same amount.

The denominator gives the fraction its name and is the number of equal parts into which the whole has been divided.

The numerator is the number of these equal parts that are to beselected or taken.

A proper fraction is one where its value is less than one, whichmeans the numerator is less than the denominator.

An improper fraction is one where its value is greater than one,which means the numerator is greater than the denominator.

Improper fractions can be converted to an integer with a proper fraction.


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Simple fractions such as the table above are easy to use and say.Decimal notation is easier to express linguistically compared to largefractions. Decimals are much easier to use in calculations, in testequipment and calculators.

Redrawing the above table with a decimal column added:English spoken & written Fraction Decimal

one eighth 0.125one quarter 0.25one third 0.333three eighths 0.375one half 0.5five eighths 0.625two thirds 0.667three quarters 0.75

seven eighths 0.875Everyone should be able to recognise and remember this table sincethese are common fractions and decimals, and are likely to come upregularly in tests and life.

On the decimal notation some fractions have come out with onedecimal digit, some with two digits and some with three digits. Thenumber of digits to the right of the decimal point is referred to as thenumber of significant places, for example:

0.5 one significant place0.25 two significant places0.625 three significant places

If you are doing calculations to three significant places, then for example: 0.5 should be written as 0.500

0.75 should be written as 0.750so that the reader knows you are working to three significant places.

It is normal, when performing a series of calculations during thesolving of a problem; to work everything out to three significant

places when the final answer is required to only two decimal places.This avoids inaccuracies in the final answer.

Please note: Leading zeros are traditionally used (0.5) but notmandatory (.5). The leading 0 is used to ensure you do not miss the

decimal point. Rules are:Following zeros (0.500) are generally dropped (0.5) unless in a

table of numbers or the working out in a problemThird digit is rounded up (0.667) if the fourth digit is over 5Third digit remains (0.333) the same if the fourth digit is 5 or less

Adding a and a equals - that is easy to perform mentally.

Adding and is (8+15) = 23 is more difficult to do mentally.24 24

It is difficult to use the fraction result, for example on a calculator or when using a tape measure or Digital MultiMeter.

In decimals the same calculation is: 0.333 +0.625

= 0.958which was easy to work out

Further, this decimal number is easier to use within the metricmeasurements of length, time, volts, etc, and when using acalculator.

In summary, in Engineering practice, when using a calculator or performing written calculations:

fractions are a more difficult notation to work withdecimals are a convenient notation to use in practice and theory

In subtraction, multiplication and division decimals are easy using acalculator, but fractions are very difficult, if not impossible, using acalculator.


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6 E XTENDED FRACTIONS AND DECIMALS

An Extended Fraction is a number comprising an integer part and afraction part:

4 33 95 269

An Extended Decimal is a number comprising an integer part and adecimal part:

4.5 33.33 95.75 269.625

In Engineering practice the Extended Decimals are easier to workwith than Extended Fractions.

Adding two Extended Decimals: 33.333+269.625

answer: +302.958

This becomes 302.96 when rounded to two significant decimalplaces.

Subtraction of one number from another is performed in a similar way:

269.625- 33.333

answer: 236.292

which becomes 236.29 when rounded to two significant decimalplaces.

A calculator is easy to use in working out Extended Decimalarithmetic such as addition, subtraction, multiplication and division.

7 P ERCENTAGE

Percentage is where a fraction or decimal number is expressedas a number compared to 100, instead of 1. To calculate thepercentage, multiply the decimal by 100, and then follow theanswer with a % symbol:

0.333 is 33.3%0.5 is 50%0.875 is 87.5%

To express a fraction as a percentage:

first convert the fraction to a decimalSecond multiply by a hundred


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All electronic components are manufactured. The accuracy of manufacture isfar from perfect. Also, a component is likely to be cheaper to make if the

accuracy of manufacture is allowed to be wide.The Buyer of Electronic Components will want to know how accurately thecomponents have been manufactured. As such, resistors, capacitors andinductors are specified with a preferred value accompanied by the tolerance.

10% tolerance, for example, indicates a 50 resistor has a value between:50-10% to 50+10%

normally written as:5010% using the symbol

Which becomes: 45 to 55 when calculated outHow exactly is this calculated out?

10% of a number is 0.1 times that number.

This is obtained by dividing 10% by 100 and removing the % symbol.

Then 5010% becomes:50-(0.1 x 50) to 50+(0.1 x50)

= 50-5 to 50+5= 45 to 55

Further examples are:

470010% = 4700-470 to 4700+470= 4230 to 5170

82,0005% = 82,000-4,100 to 82,000+4,100= 77,900 to 86,100

3302% = 330-6.6 to 330+6.6= 323.4 to 336.6


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Scientific notation is the name given to a shorthand method of writingdown long or large numbers. This method is also called Exponent

Notation.

Numbers ending with many zeros (0) can be difficult to accuratelygrasp, particularly if you are slightly dyslexic.

Scientific Notation only applies to numbers counting to a base of 10.

Example: 1,000 is written as 1 x 10 3 or just 10 3

In English we say: 10 cubed or one thousand or 10 to the power of 3

Example: 1,000,000 is written as 1 x 10 6 or just 10 6

In English we say: 10-to-the- sixth or one million or 10 to the power 6

The 10 part is called the base. The little 6 part is called the index, or power.

A positive superscript, as above, means the number is greater than 1.

A negative superscript means the number is less than 1, whichmeans it is a fraction. All of the significant digits will be to the right of

the decimal point.

Example: 1 is written as 1 x 10 -3 or just 10 -3 1000

In English we say one -thousandth. Example: 1 is written as 1 x 10 -6 or just 10 -6

1000000In English we say one -millionth.

When written out in decimal form, the two examples above are:0.001 and 0.000001

Thus, a tenth is 1 which is 10 -1 which is also 0.1 10


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This combines the use of Scientific Notation with Extended Decimals. From above we had:1,000 = 1 x 10 3

Now consider examples using Extended Decimal numbers:1.2 = 1.215 = 15180 = 1801,250 = 1.25 x 10 3 47,000 = 47 x 10 3 or 4.7 x 10 4 820,000 = 820 x 10 3 or 8.2 x 10 5 5,600,000 = 5.6 x 10 6

These are typical value ranges for resistors, voltage and power.In many ordinary maths calculations relating to, say, distance or weight:

4.7 x 10 4 8.2 x 10 5

would be acceptable, even preferable. But in electronics SI Units are expressed in

multiples or divisors of 1,000 which you will see in Section 12 on Engineering Notation.That means the correct conversions to Extended Decimals will always have 10 3, 10 6, 10 9 etc. The index is always a multiple of 3.

Decimal numbers are followed with 10 to a negative index. The index is still kept tomultiples of 3.

0.15 = 150 x 10 -3 but often left as 0.150.022 = 22 x 10 -3 0.0082 = 8.2 x 10 -3

0.000091 = 91 x 10 -6 0.0000000033 = 3.3 x 10 -9

These numbers are typical values for inductors, capacitors and current.


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Most calculations in electrical and electronic engineering require multiplyingand dividing of numbers from trillionths to trillions. The calculated result hasto be accurate and to the correct scale. It can be quite difficult to ensure thatthe answer is not out by 1,000 for example.The procedure to use is:

ensure they are expressed as a decimal number and Scientific Notation

ensure there are NO Engineering Notations mixedin (ie KW becomes 10 3 W)

do the calculations using Laws of Indices Rules below

When multiplying two numbers expressed in Scientific Notation (both to thebase of 10), you add their indices together, examples being:

10-6

x 103

= 10-6+3

= 10-3

10 9 x 10 3 = 10 9+3 = 10 12 10 -6 x 10 -9 = 10 -6-9 = 10 -15

When dividing one number in Scientific Notation by another (both to the base10), you subtract the index of the denominator from the index of thenumerator:

10 -6 / 10 3 = 10 -6-3 = 10 -9 10 9 / 10 3 = 10 9-3 = 10 6 10 -6 / 10 -9 = 10 -6+9 = 10 3

explaining in more detail:

10 -6 numerator 10 3 denominator

which is 10 -6 / 10 3 = 10 -9

Extending this to integer and decimal numbers:

2470 = 2.47 x 10 3 39000 = 39 x 10 3

815000 = 0.815 x 10 6

0.063 = 63 x 10 -3

0.00146 = 1.46 x 10 -3 0.000758 = 0.758 x 10 -3 or 758 x 10 -6

Multiplying examples:

2470 x 815000 = 2.47 x 10 3 x 0.815 x 10 6 = 2.47 x 0.815 x 10 3+6 = 2.01 x 10 9

39000 x 0.00146 = 39 x 10 3 x 1.46 x 10 -3 = 39 x 1.46 x 10 3-3 = 56.94 x 10 0 = 56.94

Dividing examples:

0.000758 / 2470 = 758 x 10 -6 / 2.47 x 10 3 = 758 / 2.47 x 10 -6-3 = 306.9 x 10 -9

815000 / 0.063 = 0.815 x 10 6 / 63 x 10 -3 = 0.815 / 63 x 10 -6+3 = 0.0129 x 10 9 = 12.9 x 10 6


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In Engineering Notation, when a number is increased or decreased by units of 1,000 it is given a name originating from the Greeks. The names, such as nano,Kilo or Mega, are only used in this full format when speaking English. The namesstart with a capital letter if greater than 1 and start with lower case letters if lessthan 1.Each name has a single letter or character symbol for use when appended to anumber. This is the short form, or abbreviated form of the Engineering notation.

Decimal Scientific Engineering Engineering full abbreviated

1.2 = 1.2 1.2 1.215 = 15 15 15180 = 180 180 180

1,250 = 1.25 x 10 3 1.25 Kilo 1.25 K

47,000 = 47 x 103

47 Kilo 47 K820,000 = 820 x 10 3 820 Kilo 820 K

5,600,000 = 5.6 x 10 6 5.6 Mega 5.6 M0.15 = 150 x 10 -3 150 milli 150 m0.022 = 22 x 10 -3 22 milli 22 m

0.0082 = 8.2 x 10 -3 8.2 milli 8.2 m0.000091 = 91 x 10 -6 91 micro 91 0.0000000033 = 3.3 x 10 -9 3.3 nano 3.3 n

The decimal notation is the normal way people write down numbers. For smallnumbers such as 1.2 or 15 it is very concise. For very large or very small numbersit becomes clumsy, such as 5,600,000 or 0.0000000033

Scientific notation is good for bringing a wide scale of numbers into a concisemanner ready for use in calculations. The engineering notation is also concise andin a form that we can easily read and speak, but is not convenient for calculations.

When carrying out electronics calculations, it is important to notehow convenient it is to:

convert from Engineering Notation to Scientific Notation

do all the calculations in Scientific Notation

convert Scientific Notation back to Engineering Notation

Note from the table above, the R has not been used for 1.2, 15or 180 as might be expected. The R is generally not usedunless you are being politically correct, as may be the case in adetailed specification with lists of components. The R is used inthe BS1852 Letter Code System for marking resistor values.


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When Noah built his ark his measurements were in Cubits - thedistance between his elbow and the tip of his outstretched fingers.Other units used over the ages were Palm, Span and Stride.

These measurements were approximate, depending on the physicalsize of the person. Equally, volumetric sizes varied - imagine buyinga small pint of beer. Standard measurements were needed, andthese evolved in the more civilised countries and regions, but stilldiffered between these regions.

In England we used miles, furlongs, yards, feet and inches for length, distance and area measurement. We used ounces, pounds,stones and hundred weight for weight measurement. Thesestandards spread across the Commonwealth and the USA.However, when it came to the basic maths for these weights andmeasurements, they were a nightmare to work with.

The length of the yard was set by King Henry I. It was decreed to bethe distance from the point of his nose to the end of his thumb. Thisis an arbitrary standard, and is typical of the origins of the EnglishSystem.

In Europe they created the metre with its variants of centimetre,millimetre and kilometre for example. The variants were all multiplesor divisors of 10, so were extremely easy to work withmathematically. The same was and is true for the gram, milligram,kilogram, and so on. The metre and kilogram are the foundations of the metric system.

An international body was set up last century to standardise on all

measurements issues covering distance, weight, time, electrical,mechanical and so on. These units are now called SI Units. SI arethe first letters of the French Systme Internationale, which isheadquartered in Paris.

On length and distance measurement the metre was adopted dueto its mathematical simplicity of being in multiples of 10. TheImperial system as originated in the UK was far too difficult interms of the inter-relationships between e.g. inch, yard, mile,furlong, hectare and acre.

The scientific community worldwide had always based itsmeasurements on the metric system, because in the 18 th and 19 th Centuries Global science was mostly European based. As a resultthe electrical SI units developed from a metric base.

The electrical SI units are listed on the attached table Units of Measurement for Voltage, Current, Resistance, Capacitance,Inductance, Power, Time, Energy and Charge. These are the mostcommon electrical measurement criteria, but there are many morecovering Electrostatics, Magnetism, Nuclear Energy and other areas.

There are still some instances where we continue to use Imperialmeasurements such as a pound of potatoes or a pint of beer.However, throughout the manufacturing and construction industrieswe are now completely metric - by law!


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There are seven Base Units of measurement asshown in the table to the right.

There are two Extended Units which relate to 2Dangle and 3D angle measurement.

All other Units of Measurement can be derived fromthese nine Units.

The quantity symbol column is the letter or symbolwe may use as an unknown variable in an equation,for example: velocity = l / t (length / time)

The unit symbol column specifies the Units of measurement, for example 60 s is 60 seconds.

If we have a situation where something is measuredin seconds, but is an unknown variable, then:

Time = t s

Feature Quantitysymbol

Unit UnitSymbol

Base Units

length l metre m

mass m kilogram kg

time t second s

electric current I amp A

temperature t kelvin K

luminous intensity I candela cd

amount of substance mol mole mol

Extended Units

plane angle radian rad

solid angle W steradian sr

Engineers use Centigrade, Scientists use Kelvin

Each degree step is the same, but the starting point is different-273 0C 0 0C 100 0C

00K 273 0K 373 0K

absolute zero water freezing water boiling

Temperature

Everyday temperatures are quoted in degrees Celsiuswhich has its 0 0C at the freezing point of water. Kelvindegrees have the same degree increments as Celsius,but start at Absolute Zero, the lowest temperaturepossible, and when atomic matter stops moving.


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Derived units are formed fromcombinations of Base Units andExtended Units.

Some important examples of mechan ica l , e l ec t r i ca l andelectronic units of measurementare provided in the table on theright.

One can play with the expressionsto change a Derived Unit from oneset of Units to another set of Units,

for example:

Volts = Watts WAmps I

= Joules/sec J/sAmps I

= Joules JAmps x seconds I s

= Joules . JCoulombs C

Also, Energy is Joules= Volts x Amps x Sec

= Watts x Sec

Feature Quantitysymbol Unit Unit Symbol Derived from

Derived Units Area A square metre m 2 m 2

Volume V cubic metre m 3 m 3 Density kilogram /cubic metre Kg / m 3 Kg / m 3 Velocity v metre / second m / s m / s

Acceleration a metre/sec/sec m / s 2 m / s 2

Force & Friction F Newton N kg m / sPressure P Pascal Pa = N / m 2 Kg / m / s

Energy E Joule J = N m kg m 2 / sPower P Watt W = J / s = N m / s kg m 2 / s 2

Electric Potential V Volts V = W / A kg m 2 / s 2 / AResistance R Ohm V / A

Conductance G Sieman S = 1 / R A / VResistivity Ohm metre m V m / A

Electric Charge Q Coulomb C A sCapacitance C Farad F A s / V

Magnetic Flux Weber Wb V sInductance L Henry H V s / A

Magnetic Flux Density B Tesla T = Wb / m 2 V s / m 2 Frequency f Hertz Hz / s

Luminous Flux L Lumen lm Cd sr Illuminance Il lux Lx = lm / m 2 Cd sr / m 2


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ElectricalUnit of Measurement

Unit of Measure- ment

trillionth 1 .

1,000,000,000,000

pico

10-12

billionth 1 .

1,000,000,000

nano

10-9

millionth 1 .

1,000,000

micro

10-6

thousandth 1 .

1,000

milli

10-3

units 1

100

thousand 1000

Kilo

103

million 1,000,000

Mega

106

billion 1,000,000,000

Giga

109

trillion 1,000,000,000,

000

Tera

1012

VoltageV Volt pV nV V mV V KV MV GV TV

CurrentI Amp pA nA A mA A KA MA GA TA

ResistanceR Ohm p n

m K M G T

Capacitance

CFarad pF nF F mF F KF

InductanceL Henry pH nH H mH H KH

Power P Watt pW nW W mW W KW MW GW TW

TimeT Second ps ns s ms s

EnergyE Joule pJ nJ J mJ J KJ MJ GJ

ChargeQ Coulomb pC nC C C C KC MC


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Normally the number notation above is used with a particular electrical unit giving an amount of volts, amps, ohms, farads, henrys,coulombs or watts.

Example: A resistor has a value of 4,700,000 ohms. Answer: It is written as 4.7M , and in English we say 4.7 meg Ohms.

Example: A capacitor has a value of 68 trillionths of a Farad Answer: It is written as 68 pF, and in English we say 68 pico Farads.

Example: A lightning strike is measured at 250 million volts Answer: It is written as 250 MV, and in English we say 250 mega Volts.

Example: A radio aerial coil is 80 x 10 -3 Henrys Answer: It is written as 80 mH, and in English we say 80 milli Henrys.

Example: The current through a circuit is 0.0000025 Amps Answer: It is written as 2.5 A, and in English we say 25 micro Amps.

Example: An electric fire consumes 3 thousand Watts Answer: It is written as 3 KW, and in English we say 3 Kilo Watts.

Example: The charge held in a capacitor is 0.0000000055 Coulombs Answer: It is written as 5.5 nC, and in English we say 5.5 nano Coulombs.

Example: What is the voltage across a 27 K resistor with a 65 mA currentflowing through it?

Answer: Ohms Law V = IR = 27K x 65m = 27 x 10 3 x 65 x 10 -3 = 27 x 65 x 10 3-3 = 1755 V

Example: What charge is transferred in 100 ms with a 22 A current flowing?Answer: Q = I x t = 22 A x 100 ms = 22 x 10 -6 x 100 x 10 -3

= 22 x 100 x 10 -6-3 = 2200 x 10 -9 = 2.2 x 10 -6 = 2.2 C

19 NOTE ON CALCULATOR USE :

Most calculators, even the simple ones below 5,have a squares button and a square root button.They also have + (plus), - (minus), x (multiply),divide (/) and = (equals) buttons. In real life, thismakes calculating the above squares and square-roots quite easy and accurate.

Many calculators have Scientific notation buttons,but their results are often wrong for some reason,for example 10 6 x 10 -3 = 10 3 , but is given as 10 2.

20 NOTE ON COMPUTER USE :

Microsoft WORD software package supportsScientific Notation for square and square-root (10 2 and 10 -2) and other superscript indices.

Fractions and equations can be more effectivelywritten in Word using an extra mini-add-in softwarepackage called MathType from Design Science Inc.The basic version of this package is free and willcover most C&G and Edexcel BTEC needs.


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Many simple electrical circuit calculations are based on Ohms Law:

V = R V = IR I = VI R

When you multiply 1 by 1, the answer is 1 10 0 x 10 -0 = 1When you multiply 10 by 0.1, the answer is 1 10 1 x 10 -1 = 1When you multiply 100 by 0.01, the answer is 1 10 2 x 10 -2 = 1When you multiply 1000 by 0.001, the answer is 1 10 3 x 10 -3 = 1

In a similar way: K x mA = V 10 3 x 10 -3 = 1

i.e. the thousand Ohms and the thousandth Amps cancel each other out.

Example: 20 Volts = 5 mA4 K

Example: 100 Volts = 5 K 20 mA

Example: 2 K x 12 mA = 24 Volts

Noting: Volts is often written as Volts, sometimes abbreviated to V

mA is standard for milli AmpsK is standard for thousand Ohms

Further Note:

In every day electrical, telephone, control and electronicsituations the voltage range is generally between 3 V and300 V, either DC or AC.

From Ohms Law: V = I x R so if R is in the units / tens / hundreds range,

I is likely to be units

if R is in the K range, I is likely to be mA range

if R is in the M range, I is likely to be A range

Example: 22 K x 4.9 mA = 108 Volts

Example: 9.1 K x 42.5 mA = 387 Volts

Example: 4.7 M x 2.5 A = 11.75 Volts

Example: 56 M x 72 A = 4 KV

E1 02 Measurement & Scale V6

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