module07.ppt

AA m e r i c a nm e r i c a n WW e l d i n ge l d i n g S S o c i e t yo c i e t y

Module 7 - Module 7 - 11

Module 7Module 7

Metric Practices for Metric Practices for Welding InspectionWelding Inspection



Metric SystemMetric System

Le SystemLe System

InternationaleInternationale

d’Unitesd’Unites

or :or :

SISI



Resistance to SIResistance to SI EconomicEconomic UnfamiliarityUnfamiliarity Not invented hereNot invented here Requires effortRequires effort Others?Others?



SI AdvantagesSI Advantages Simple base unitsSimple base units Worldwide usageWorldwide usage Based on powers of 10Based on powers of 10 Simple decimal systemSimple decimal system



ANSI/AWS ANSI/AWS A1.1 - 98A1.1 - 98



U.S. Customary SystemU.S. Customary System ComplicatedComplicated AwkwardAwkward ConfusingConfusing Used only by U.S.Used only by U.S.

But we are familiar with it, and we But we are familiar with it, and we love it!love it!



U.S. System - 1 of 2U.S. System - 1 of 2

Length - Inch, foot, yard, etc.

Mass - Ounce, pound, ton, etc.

Volume- Ounce, pint, quart, etc

Area - Square feet, acre, etc

Others - Various units



U.S. System - 2 of 2U.S. System - 2 of 2

Conversion factors are not in Conversion factors are not in multiples of 10multiples of 10

12 inches per foot12 inches per foot 36 inches per yard36 inches per yard 5,280 feet per mile5,280 feet per mile 1,760 yards per mile1,760 yards per mile et cetera, et ceteraet cetera, et cetera


Module 7 - Module 7 - 99SI System - Table 7.1SI System - Table 7.1Only one unit for each type of Only one unit for each type of

measurementmeasurement

Length - Meter

Mass - Kilogram

Volume- Liter

Area - Square meters

Others - One base unit



AWS SI VersionAWS SI Version

Note: The true SI system uses the Note: The true SI system uses the gram (g) for mass but AWS in A1.1-gram (g) for mass but AWS in A1.1-98 has selected the kilogram (kg) as 98 has selected the kilogram (kg) as the base unit for mass. This was the base unit for mass. This was done to simplify the welding usage done to simplify the welding usage of mass.of mass.


Module 7 - Module 7 - 1111SI System Prefixes - Table SI System Prefixes - Table 7.27.2

Based on powers of 10 Based on powers of 10

Preferred units in multiples of 10Preferred units in multiples of 1033

KiloKilo -- k k - - 1,0001,000 -- 101033

MegaMega -- M -M - 1,000,0001,000,000 -- 101066

MilliMilli -- mm - - 1/1,0001/1,000 -- 1010-3-3

MicroMicro -- - - 1/1,000,000 -1/1,000,000 - 1010--

66


Module 7 - Module 7 - 1212SI Welding Units - Table SI Welding Units - Table 7.37.3

Deposition rateDeposition rate kg/hrkg/hr Flow rateFlow rate L/minL/min Tensile strengthTensile strength MPaMPa Travel speedTravel speed mm/smm/s Wire feed speedWire feed speed mm/smm/s PressurePressure kPakPa


Module 7 - Module 7 - 1313Positive & Negative Numbers Positive & Negative Numbers - 1 of 2- 1 of 2

Addition and Addition and SubtractionSubtraction

5 added to 7 = 125 added to 7 = 12 11 minus 6 = 511 minus 6 = 5 5 added to a -7 = -25 added to a -7 = -2

a -3 added to a -a -3 added to a -4 = -74 = -7

5 minus a -8 = 5 minus a -8 = +13+13

a -8 minus a -4 = a -8 minus a -4 = -4-4

a -9 minus 6 = -a -9 minus 6 = -1515


Module 7 - Module 7 - 1414Positive & Negative Numbers Positive & Negative Numbers - 2 of 2- 2 of 2

Multiplication and DivisionMultiplication and Division (-6) x (-5) = +30(-6) x (-5) = +30 (-5) x (3) = -15(-5) x (3) = -15 (-6) ÷ (2) = -3(-6) ÷ (2) = -3 (8) ÷ (-4) = -2(8) ÷ (-4) = -2 (-9) ÷ (-3) = +3(-9) ÷ (-3) = +3



Scientific NotationScientific NotationSNSN

““Writing a number such that the Writing a number such that the decimal point is always moved to the decimal point is always moved to the immediate right of the first digit not immediate right of the first digit not zero, and its relative size expressed zero, and its relative size expressed

as an exponent (power of ten).”as an exponent (power of ten).”


Module 7 - Module 7 - 1616Exponents - Positive Exponents - Positive Powers of 10Powers of 10

101000 = 1 (by definition. Any number raised = 1 (by definition. Any number raised to a zero power equals 1 ; e.g., 58to a zero power equals 1 ; e.g., 5800 = = 1)1)

101011 = 10 = 10 101022 = 100 = 100 101033 = 1,000 = 1,000 101066 = 1,000,000 = 1,000,000

Positive Exponents = Numbers greater than 1Positive Exponents = Numbers greater than 1


Module 7 - Module 7 - 1717Exponents - Negative Exponents - Negative Powers of 10Powers of 10

101000 = 1 (by definition. Any number = 1 (by definition. Any number raised raised to a zero power equals 1 ; to a zero power equals 1 ; e.g., 25e.g., 2500 = 1) = 1)

1010-1-1 = 0.1 = 0.1 read as ‘one tenth’read as ‘one tenth’ 1010-2-2 = 0.01 = 0.01 read as ‘one hundredth’read as ‘one hundredth’ 1010-3-3 = 0.001 = 0.001 read as ‘one thousandth’read as ‘one thousandth’ 1010-6-6 = 0.000001 = 0.000001 read as ‘one millionth’read as ‘one millionth’

Negative Exponents = Numbers less than 1Negative Exponents = Numbers less than 1



SN ExamplesSN Examples

234 234 = 2.34 x 102= 2.34 x 102

5,678 5,678 = 5.678 x 103= 5.678 x 103

0.0234 0.0234 = 2.34 x 10-2= 2.34 x 10-2

0.000567 0.000567 = 5.67 x 10-4= 5.67 x 10-4

In the first In the first answeranswer example above, example above, 2.34 is called the ‘root’, 10 is the 2.34 is called the ‘root’, 10 is the ‘base’, and the 2 is the exponent‘base’, and the 2 is the exponent



SN AdvantagesSN Advantages Simplifies very large numbersSimplifies very large numbers Simplifies very small numbersSimplifies very small numbers A decimal systemA decimal system Based on powers of tenBased on powers of ten Simplifies calculationsSimplifies calculations



Conversion Example 1 & 2Conversion Example 1 & 270,000 psi = ?? Pa (1 psi = 6,895 70,000 psi = ?? Pa (1 psi = 6,895

Pa)Pa)

70,000 x 6,895 = 482,650,000 Pa70,000 x 6,895 = 482,650,000 Pa

= 4.8265 x 10= 4.8265 x 10+8+8 Pa Pa

But UTS in metric is usually given in Mpa. So,But UTS in metric is usually given in Mpa. So,

70,000 psi = ?? Mpa (1 psi = 6.895 x 1070,000 psi = ?? Mpa (1 psi = 6.895 x 10-3-3 MPa)MPa)

(70,000) x (6.895 x 10(70,000) x (6.895 x 10-3-3 ) = 482.65 MPa ) = 482.65 MPa



For the number: 1,234,567.987654

Number Position & Name - Number Position & Name - Ex. 3Ex. 3

To the left of the To the left of the decimal :decimal :

7 in units position7 in units position 6 in tens position6 in tens position 5 in hundreds position5 in hundreds position 4 in thousands position4 in thousands position 3 in ten thousands3 in ten thousands 2 in hundred thousands2 in hundred thousands 1 in millionths position1 in millionths position

To the right of the To the right of the decimal :decimal :

9 in tenths position9 in tenths position 8 in hundredths position8 in hundredths position 7 in thousandths position7 in thousandths position 6 in ten thousandths6 in ten thousandths 5 in hundred thousandths5 in hundred thousandths 4 in millionths4 in millionths


Module 7 - Module 7 - 2222Exponential Multiplication Exponential Multiplication - Ex. 4- Ex. 4

Multiply the two roots in the normal fashion, Multiply the two roots in the normal fashion, and then add exponent powers to get exponent and then add exponent powers to get exponent value :value :

(2.0 x 10(2.0 x 1033) x (1.5 x 10) x (1.5 x 1055) = 3.0 x 10) = 3.0 x 1088

(1.0 x 10(1.0 x 1088) x (4.5 x 10) x (4.5 x 1077) = 4.5 x 10) = 4.5 x 101515

(3.5 x 10(3.5 x 10-3-3) x (2.0 x 10) x (2.0 x 1066) = 7.0 x 10) = 7.0 x 1033

(5 x 10(5 x 1022) x (12 x 10) x (12 x 10-6-6) = 60 x 10) = 60 x 10-4-4 or, as or, as follows:follows:

= 6.0 x 10= 6.0 x 10-3-3


Module 7 - Module 7 - 2323Exponential Division - Ex. Exponential Division - Ex. 55

Divide the two roots in the normal Divide the two roots in the normal fashion, and then subtract the second fashion, and then subtract the second exponent from the first to get final exponent from the first to get final exponent value :exponent value :

(3.0 x 10(3.0 x 1044 ) ÷ (1.5 x 10 ) ÷ (1.5 x 1022 ) ) = 2.0 x 10 = 2.0 x 1022

(6.0 x 10(6.0 x 10-7-7 ) ÷ (3.0 x 10 ) ÷ (3.0 x 1033 ) ) = 2.0 x 10 = 2.0 x 10 -10-10

(4.5 x 10(4.5 x 1044 ) ÷ (1.5 x 10 ) ÷ (1.5 x 10 -5-5 ) ) = 3.0 x 10 = 3.0 x 1099

(8.0 x 10 (8.0 x 10 -6-6 ) ÷ (2.0 x 10 ) ÷ (2.0 x 10 -9-9 ) = 4.0 x 10 ) = 4.0 x 1033


Module 7 - Module 7 - 2424Addition With Exponents - Addition With Exponents - Ex. 6Ex. 6

Same exponent required prior to adding; Same exponent required prior to adding; usually change the exponent of the smaller usually change the exponent of the smaller value for ease of operation :value for ease of operation :

(2.3 x 10(2.3 x 1044 ) + (3.54 x 10 ) + (3.54 x 1055 ) ) = ?? = ??

(0.23 x 10(0.23 x 1055 ) + (3.54 x 10 ) + (3.54 x 1055 ) ) = 3.77 x 10 = 3.77 x 1055

(3.78 x 10(3.78 x 10-6 -6 ) + (7.45 x 10) + (7.45 x 10-4-4 ) = ?? ) = ??

(0.0378 x 10(0.0378 x 10-4-4 ) + (7.45 x 10 ) + (7.45 x 10-4-4 ) = 7.4878 x ) = 7.4878 x 10 10 -4-4


Module 7 - Module 7 - 2525Subtraction With Exponents Subtraction With Exponents - Ex. 7- Ex. 7

Same exponent required prior to adding; Same exponent required prior to adding; usually change the exponent of the usually change the exponent of the smaller value for ease of operation :smaller value for ease of operation :

(7.8 x 10(7.8 x 1066 ) - (9.4 x 10 ) - (9.4 x 1044 ) ) = ??= ??

(7.8 x 10(7.8 x 1066 ) - (0.094 x 10 ) - (0.094 x 1066 ) ) = 7.706 x 10= 7.706 x 1066

(3.9 x 10(3.9 x 10-4-4 ) - (6.1 x 10 ) - (6.1 x 10 -5-5 ) ) = ?? = ??

(3.9 x 10 (3.9 x 10 -4-4 ) - (0.61 x 10 ) - (0.61 x 10 -4-4 ) )= 3.29 x 10 = 3.29 x 10 -4-4



Rounding Off RulesRounding Off Rules Rule 1Rule 1 - Increase the last retained - Increase the last retained

digit by one if the next digit to its digit by one if the next digit to its right is 5 or largerright is 5 or larger

Rule 2Rule 2 - Retain the last digit - Retain the last digit unchanged if the next digit to its unchanged if the next digit to its right is less than 5.right is less than 5.



Rounding Off - Example 8Rounding Off - Example 8

8,937 = 9,0008,937 = 9,000 Rounded to the Rounded to the nearest thousandnearest thousand

8,937 = 8,9008,937 = 8,900 Rounded to the Rounded to the nearest hundrednearest hundred

8,937 = 8,9408,937 = 8,940 Rounded to the Rounded to the nearest tennearest ten



Rounding Off - Example 9Rounding Off - Example 9

4.4638 = 44.4638 = 4 Rounded to the nearest Rounded to the nearest unitunit

4.4638 = 4.54.4638 = 4.5 Rounded to the nearest Rounded to the nearest tenthtenth

4.4638 = 4.464.4638 = 4.46 Rounded to the Rounded to the nearest hundredthnearest hundredth

4.4638 = 4.464 Rounded to the nearest 4.4638 = 4.464 Rounded to the nearest thousandththousandth



Rounding ErrorsRounding Errors

““Rounding should always be done in Rounding should always be done in a single step to avoid rounding a single step to avoid rounding

errors.”errors.”



Metric PrefixesMetric Prefixes

““Metric prefixes can substitute for Metric prefixes can substitute for the exponential form to simplify the exponential form to simplify

handling large or small numbers.”handling large or small numbers.”



Metric Prefix Example 10Metric Prefix Example 10

456,000,000 Pa456,000,000 Pa = 456 = 456 MPaMPa

56 km56 km = 56,000 = 56,000 mm

234,000 mm234,000 mm = 234 m= 234 m

456 g456 g = 0.456 kg= 0.456 kg



Conversion FactorsConversion Factors

““To aid in converting values from To aid in converting values from one system to another, conversion one system to another, conversion

tables have been prepared.”tables have been prepared.”



Conversion Example 11Conversion Example 11

Convert 40.0 psi to kPaConvert 40.0 psi to kPa

Conversion factor, psi to kPa = 6.895Conversion factor, psi to kPa = 6.895

40.0 x 6.895 = 275.8 kPa40.0 x 6.895 = 275.8 kPa

275.8 kPa rounds to 2.76 x 10275.8 kPa rounds to 2.76 x 1022 kPa kPa




Convert 625 MPa to psiConvert 625 MPa to psi

Conversion factor, MPa to psi = 1.450 x Conversion factor, MPa to psi = 1.450 x 101022

625 MPa x 1.450 x 10625 MPa x 1.450 x 1022 = = 906.25 x 10906.25 x 1022

= 9.06 x 10= 9.06 x 1044 psi psi




Convert 5/32” (0.156”) to mmConvert 5/32” (0.156”) to mm

Conversion factor, inches to mm = Conversion factor, inches to mm = 25.425.4

0.156 x 25.4 0.156 x 25.4 = 3.9624 mm= 3.9624 mm

= 3.96 mm= 3.96 mm




Convert 7.3 kg/h to lb/hConvert 7.3 kg/h to lb/h

Conversion factor, kg/h to lb/h = Conversion factor, kg/h to lb/h = 2.2052.205

7.3 x 2.205 7.3 x 2.205 = 16.0965 lb/h= 16.0965 lb/h

= 16 lb/h= 16 lb/h



Temperature ConversionTemperature Conversion

Convert 100Convert 10000 C to C to 00FF

Conversion Factor (formula) is :Conversion Factor (formula) is :

((00C x 1.8) + 32C x 1.8) + 32 = = 00FF

(100 x 1.8) + 32 = 180 + 32(100 x 1.8) + 32 = 180 + 32

= 212 F= 212 F



Temperature ConversionTemperature Conversion

Convert 100Convert 10000 F to F to 00CC

Conversion Factor (formula) is :Conversion Factor (formula) is :

((00F - 32) ÷ 1.8F - 32) ÷ 1.8 = = 00CC

(100 - 32) ÷ 1.8 = 68 ÷ 1.8(100 - 32) ÷ 1.8 = 68 ÷ 1.8

= 37.8 = 37.8 00CC



Style and Usage - A1.1Style and Usage - A1.1 Use prefixes where possibleUse prefixes where possible Use steps of 1,000Use steps of 1,000 Do not mix, unless warrantedDo not mix, unless warranted Capitalization rulesCapitalization rules PluralsPlurals PunctuationPunctuation Number groupingNumber grouping

module07.ppt

Documents

small numbers

negative numbers

temperature conversionconvert 1000

positive

normal fashion

number raised

power equals 1

base unit