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SAP Note

Header Data

Symptom

There are rounding problems when using product units of measure.

Other Terms KZWSO, KZWSM, XU033, XU056, XU040, MURC, T006

Reason and Prerequisites

This note describes the conversion with product units of measure and gives recommendations on howyou can avoid rounding problems.

Solution

1. General information on the quantity conversion in the SAP System

a) Base unit of measure and alternative units of measure

The base unit of measure is the unit of measure which is used to manage thestocks of the material.The system converts all quantities which you enter in other units of measure(alternative units of measure) into the base unit of measure.

To be able to convert a quantity whose unit of measure is not the same as thebase unit of measure into the base unit of measure, the system requires a conversion factor.

Quantity in base unit of measure = Quantity in alternative unit of measure *conversion factor

b) Numerator and denominator

The values of the conversion factors are saved as the quotient. The numeratorand denominator of the quotient are whole numbers with a maximum of 5 places.

Example 1: Numerator and denominator

The alternative unit of measure is piece (PCS). The base unit of measure iskilo (KG). 3 pcs weigh 5 KG, that is, the conversion ratio is 3 pcs = 5 KG.

The resulting conversion factor is: 5/3 KG/PCS

The quotient of the conversion factor is defined such that the numerator ofthe quantity in the base unit of measure corresponds to the denominator of the quantity in thealternative unit of measure.

Therefore, the quotient here is also 5/3: the numerator is 5 and thedenominator is 3.

Example 2: Whole number numerators and denominators

The numerator and denominator are in integer form, that is, if 3.14 M2corresponds to one piece, this must be represented as 314 M2 = 100 PCS or reduced, 157 M2 = 50 PCS.

In general, decimal conversion factors can be transferred exactly toquotients by means of a continued fraction development (this applies to finite and periodic decimal

362932 - Conversion with proportion/product units

Version 28 Validity: 24.06.2004 - active Language English

Released On 24.06.2004 12:57:13

Release Status Released for Customer

Component LO-BM-UOM Batch-Specific Units of Measure

BC-SRV-ASF-UOM Unit Management LO-BM-AI Active Ingredients

MM-IM-GF-AUM Alternative Units of Measure

Priority Recommendations / Additional Info

Category Consulting

Other Components



fractions only, while as a rule conversion factors do meet this requirement).

Approximations for a decimal fractions can be obtained by a prematuretermination of the continued fraction development. In the quantity conversion environment, thecriterion for a termination is the maximum number of places for numerator and denominator.

Using ABAP function CONVERT_TO_FRACT5, you can obtain the best approximationfor a given decimal fraction as a quotient with maximally 5-digit numerator and denominator.

If the continued fraction development results in an approached decimalfraction, this decimal fraction is generally cyclic and can therefore not be represented with finitenumber of places.

In any case, the numerator and denominator as a result of a continuedfraction development do not have the same factors.

Literature: Knuth, D.E.: The Art of Computer Programming, Volume 2, Seminumerical Algorithms, Second Edition.Reading: Addison-Wesley 1981. S. 313-315, 339-341, 363 (40. and 43.).

Example 3: Too large numerators and denominators

When 120000 CM3 = 0,2 tons (TO), you can no longer save numerator anddenominator of conversion ratio 600000 CM3 = 1 TO as numerator and denominator may have maximallyfive digits.

Here, you must either select a larger volume unit or a smaller unit ofweight: With DM3 the conversion ratio would be 600 DM3 = 1 TO, with KG the conversion ratio would be600 CM3 = 1 KG.

Generally, the alternative units of measure and the base unit of measureshould result in quantities that are in the same dimension since the conversion factors may not belarger than 99999/1 and not smaller than 1/99999.

c) Choosing the base unit of measure

When choosing the base unit of measure, you should take the following intoaccount:

¡ If the base unit of measure is selected too small, quantities or values might become toolarge (see Example 4a).

¡ The larger you select the base unit of measure to be, the more "inaccurately" the system can

manage the stocks (see Example 4b).

¡ If the base unit of measure shall be a dimensionless unit (a packing unit such as piece,box, and so on), you must select the smallest of the dimensionless units of measure as abase unit of measure (see Example 5).

Basically, the same applies for dimension afflicted (physical) units of measure: The baseunit of measure is supposed to be a unit of a certain dimension (for example a length), andboth metric and non-metric units are used (for example meter and foot), then you shouldselect the smallest of the used dimension afflicted units as a base unit of measure. This isnot obligatory, because quantities in physical units of measure generally are - and alsoshould be - granted to decimal places; however, you should note in any case that the sameeffects occur as described in example 5.

When you use of metric and non-metric units of measure, it is recommended to set the numberof the rounding decimal places for these dimension afflicted units of measure to 3 (as thenumber of the decimal places of the quantity fields) in order to avoid different side

effects as the system does not round in the same way in all transactions (see also section1.d).

¡ The base unit of measure can no longer be changed (see Note 138767).

Example 4a: Stock quantities are too high because the base unit of measure istoo small

If you select the base unit of measure too small, the system might no longerbe able to represent stock quantities with the available places. As quantities are generally alsolinked to values, the number of places for the value items should also be taken into account.

A paper material is lead up to now in PCS (= individual sheets ofpaper).Since no individual PCSs are generally sold, the new unit of measure TPC (= a thousand

pieces) has instead been defined.

Example 4b: Accuracy limit of the base unit of measure

For example, if a material is managed in TO, the accuracy with which stockscan be managed is 1 KG (with 3 decimal places for quantity fields).



Example 5: Dimensionless base unit of measure (Packing unit)

The example from Note 122471 is used as a basis and placed in this contextset: A material is managed in boxes (BOX). There is an alternative unit of measure PCS. Theconversion ratio is 24 PCS = 1 BOX.

It does not result in any rounding problems when you post multiples of 3 PCS= 0.125 BOX (with 3 decimal places for quantity fields). In the following, this conversion ratiowill be specified as "Increment".

If you want to post per piece, you must consider the following:

Goods movements should not be posted in units of measure that are smallerthan the base unit of measure if they are not multiples of the increment.

For example, you enter a goods receipt of 13 PCS, the system stores 0.542 BOXin the stock (13 / 24 = 0.54166666...).

If you then want to display the stock in PCS, 13.008 PCS are displayed (0.542* 24 = 13.008).

This effect is caused because the stock is exclusively managed in base unitsof measure, quantity fields with finite decimal places are saved and if the alternative unit ofmeasure is smaller than the base unit of measure. In other words: The representation of quantitiesfrom PCS to BOX and back to PCS is not unique for quantities that are not multiples of theincrement.

If you enter a goods receipt in base unit of measure - or an alternative unitof measure that is larger than the base unit of measure (e.g. pallets) - , the system does no longergenerate rounding errors (however, it may nevertheless come to quantities in PCS with decimalplaces, if not multiples of the increment are posted).

In order to avoid the above described situation, if possible, you shouldselect the smallest unit of measure as a dimensionless base unit of measure so that the alternativeunits of measure are a multiple of the base unit of measure.

If you now select the smallest unit of measure as a base unit of measure, thesystem does no longer generate rounding errors with goods movements in PCS (Base unit of measure) orin BOX (Alternative unit of measure). However, quantities in BOXes which are not multiples of theincrement will still result in quantities in PCS with decimal places (instead of 0.333 BOX = 7.992PCS you need to post 8.000 PCS -> 0.333 BOX).

In addition, you must now take the following into account: You can at leastonly post the quantities in alternative unit of measure as a complete stock removal which aremultiples of the increment. In other words: Postings of complete stock removals of quantities inalternative units of measure which are larger than the base unit of measure generally result inpositive or negative remaining quantities.

For example, if 13 PCS are contained in the stock, this can be displayed inthe stock overview as 0.542 BOX. If you now want to post 0.542 CR as goods issue, this will resultin an error as a negative remaining quantity of 0.008 PCS would be created.

Remark: This example applies in the same way to metric and non-metric units of measure of the samedimension, as well as for units of measure of different dimensions. In these cases, the quantitiesin alternative unit of measure are mostly not multiples of the quantity in base unit of measure.

Conclusion: Mostly, all quantities that are not multiples of the increment cannot be converted uniquely intoeach other. Among other things, the effects described in example 5 and example 8.2 will occur.Regarding "one-to-one" and on the general calculation of the increment also refer to section 2.e.

d) Maintaining the units of measurement

During the maintenance of the units of measure (Transaction CUNI) foravoiding or minimizing conversion errors you must consider the following:

¡ The conversion factor, consisting of numerator, denominator, and exponent, should bemaintained in such a way that the exponent is Zero, and numerator and denominator havemaximally five digits, as in most transactions there is a restriction to this number ofplaces.

¡ The entered numerator and the denominator are not reduced, that is, they are notautomatically divisor-external. SAP recommends to maintain numerator and denominatordivisor-externally as the quotient is not always reduced within the system before it isconverted. In case of large quantities and long numerators or denominators the system mightgenerate conversion errors due to the limited number of places of data types (with floatingpoint numbers in SAP Systems with double accuracy according to the IEEE 754 standard, for

example, only the first 15 decimal places can be displayed reliably). The smaller numeratorand denominators are, the larger the quantities that can be converted without roundingerrors.

¡ No cross-dimension check of the conversion factors occurs. For example are 381 M = 1250 FT.From this follows 145161 M2 = 1562500 FT2. Mostly, however, certain approximate values thatare not consistent for the respective units of length are maintained for the non-metricsurface units of measure. For the conversion with non-metric units refer to Note 23771.

¡ Please consider the two fields for the decimal places: For example the display decimal place



is taken into account in the list output; onto the rounding decimal place, for example, itis rounded during the creation of a production order. The rounding decimal place is not,however, considered by every transaction so that particularly in the case of a simultaneoususe of metric and non-metric units it is recommended to set the rounding decimal places ofthese units of measurement to 3 (like the number of the decimal places of the quantityfields). Additional information is available in Note 77525.

¡ A unit of measurement family can be used unrestrictedly, for example to limit the selectablephysical alternative units of measure during the use of the variant configuration.

¡ In a SAP system group of several SAP Systems the settings must be equal for all used unitsof measurement. Please refer to Notes 492979 and 595742.In case of connecting Non-SAP Systems, you must adjust the settings on each other.

2. Batch-specific units of measure - product units of measure

The batch-specific material unit of measure is an alternative unit of measure of amaterial for which the conversion ratio into the base unit of measure can be defined batch-specifically.

Whereas for the other alternative units of measure, the conversion ratio is predefinedin the material, you define the planned (average) conversion factor for the batch-specific materialunits of measure in the material and the actual conversion factor into the base unit of measure onthe batch.

You use batch-specific units of measure if the conversion ratio of the unit of measureinto the base unit of measure can be different for different batches of a material.

Batch-specific material units of measure can be proportional or product units of

measure.

a) Characteristic for saving the conversion factor

The conversion factor between a batch-specific material unit of measure andthe base unit of measure is saved as a valuation of a characteristic in the batch classification.The conversion factor is saved as a finite decimal fraction with a maximum of 15 digits (placesbefore and after the decimal point). The actual conversion factor is a quotient which is derivedinternally from the stored decimal fraction (see section "Displayability of the conversion factor asa five-digit fraction" further below).

Remark: Numeric characteristic valuations are stored internally as floating point number. When storingcharacteristic valuations in numeric format in the database, the values are rounded to the formatdefined by the template. For this reason, when newly creating batch classifications, values maydiffer from the values stored in the database afterwards. Therefore, calculated numeric values whichare used in the dependency for further calculations (e.g. for calculating a conversion factor) must

be rounded explicitly to the format defined in the characteristic in the dependency!In this connection, please also refer to Note 399308 which describes this subject for variantconfigurations: In particular, classification and configuration valuations differ from numericcharacteristics in the database.

In addition, the following facts which have to be considered in borderlinecases are to be noted:When storing in and subsequently reading from the database, the original floating point number isnot returned in all cases.This behavior occurs for certain values, where those values differ (depending on the implementation)for the databases used. This behavior is not caused by a database error, however, but by a missingdefinition in the SQL standard.The SQL standard determines that the accuracy of floating point numbers is to be guaranteed up to 15places after the decimal point. It does not define that the floating point numbers returned by thedatabase are to be rounded to the IEEE 754 standard with double accuracy. This is the reason why theunambiguity during storage in databases is presently not guaranteed for floating point numbers inthe SAP environment.

The program coding in the correction from Note 680228 may serve as a template for a correspondingrounding logic in a variant function.

Example 6: Decimal fraction

The base unit of measure of a material is kilo and the product unit ofmeasure is piece. 3 PCS of the batch have a weight of 10 KG. The conversion factor delivers theperiodic decimal fraction 3.33333333 ... KG/PCS (if PCS is defined as the leading product unit ofmeasure for goods receipt in the material master).

In this example, the format of the characteristic for the conversion factoris defined as numeric without exponential display with a total of 8 digits and 3 decimal places.This allows exact posting by pieces, and the resulting conversion factor is 3.333 KG/PCS (see alsofurther below: case 1A with example 7).

b) What does the accuracy of the conversion depend on?

The accuracy of the conversion depends on several factors:

¡ Number of rounding decimal places of the alternative unit of measure

¡ Number of rounding decimal places of the base unit of measure



¡ Value or number of places of the conversion factor (the rounding decimal places of the unitof measure [that is defined in the characteristic of the conversion factor] are not analyzedby the system; usage in the object dependencies of the classification is possible)

Case 1A: Product units of measure in whole numbers (0 rounding decimalplaces)

If you are using (countable) product units of measure in whole numbers as apiece, package or role and the base unit of measure is a unit of measure such as meters, kilogram,or square meters, then you use the same number of decimal places in the conversion characteristic asthe number of rounding decimal places in the base unit of measure.

The conversion factor must not have more than this number of decimal placesbecause otherwise, the one-to-one is no longer ensured during the conversion of PCS into the baseunit of measure and back for all multiples of 1.

You define the conversion factor with "Calculation basis- fromproportion/product unit of measure" as follows as a fraction:

Conversion factor = Base unit of measure / Product unit of measure

With that, the rounding differences described in example 8.2 do not occur inthe SAP system. However, the quantity in base unit of measure can easily deviate from reality.

Example 7: Diverging quantity in base unit of measure

You enter a goods receipt of 3 piece. The total weight is 10 KG.In the SAPsystem, the conversion factor is stored with 3.333 KG/PCS, in the case that KG is defined with 3rounding decimal places. Then the quantity in the base unit of measure in the system is 9.999 KG andnot 10 KG.

Case 1B: Product units of measure with less than 3 rounding decimal places

Definition:

N = Rounding decimal places Base unit of measure

- Rounding decimal places Product unit of measure

The conversion factor should have, at the most, N decimal places to avoid rounding errors.

Remark: This rule is only useful for product units of measure that have less than 3 rounding decimal placessince the quantity in product unit of measure is rounded in case of 3 rounding decimal places duringthe one-to-one check of the application (see below).

Example 8: Determining the number of decimal places of the conversion factorbetween base unit of measure KG and the product unit of measure TPC (one thousand pieces)

N = rounding decimal places KG - rounding decimal places TPC

= 3 - 2 = 1

If you use a conversion factor with 1 decimal place, no rounding errors occurwhen multiples of 0.01 TPC = 10 PCS are posted.

Example 8.1:

The conversion factor is 3.3 KG/TPC.

0.01 TPC = 10 PCS weighs 0.033 KG. 0.03 TPC = 30 PCS weighs 0.099 KG.

Example 8.2:

If you use a conversion factor with 2 decimal places, rounding errors occur:

The conversion factor is 3.33 KG/TPC.

Goods receipt 0.03 TPC = 0.0999 KG (is rounded off to 0.100 KG)

Goods issue 0.01 TPC = 0.0333 KG (is rounded off to 0.033 KG)



0.01 TPC = 0.0333 KG (is rounded off to 0.033 KG) 0.01 TPC = 0.0333 KG (is rounded off to 0.033 KG)

As a result of the rounding error, a residual quantity of 0.001 KG remains in the stock.

Remark: If multiples of 0.1 TPC = 100 PCS would be posted, then all entry quantities would be convertableone-to-one into the base unit of measure in this case, and no rounding differences would occur. Thiscan be achieved if a product unit of measure TPC (one thousand pieces) is defined with 1 roundingdecimal place.

Case 2: Product units of measure with 3 rounding decimal places

If you use product units of measure with 3 rounding decimal places such as

kilograms, barrels, square meters, or meters, you should use a conversion characteristic with thehighest degree of accuracy possible:

Select the standard exponential display: the numeric characteristic shouldthen have a total of 15 places and have a maximum number of 14 decimal places.

Then, if the exponential display is too inconvenient for your end user, thenyou can also use a normal decimal format as a fixed point number with a total of 15 places dependingon the value range of the conversion factor. Create the number of decimal places such that thenumber of predecimal places is defined so that the largest factor is just displayable (more than 5predecimal places does not make sense because the conversion factor must never be larger than99999/1).

Example 9: Square meter and kilo

You enter a goods receipt of 3 M2 with a total weight of 4 KG.

The conversion factor 1.33333 ... KG/M2 should be stored as exactly aspossible.

A factor of 1.33333333333334E+00 KG/M2 results in the standard exponentialdisplay.

You can also define the conversion factor in normal decimal format. Themaximum factor is less than 10 KG/M2. The conversion factor should be created as follows:

"Number places" = 15

"Number decimal places" = 14

c) Where are the rounding decimal places defined for the quantities and what effects doesthis have?

The rounding decimal places are defined in Customizing for the units ofmeasurement via "Number of rounding decimals" (Transaction CUNI).

For materials with product units of measure, a verification of the postedquantities is carried out:For 3 rounding decimal places, the one-to-one of the conversion of the quantity is checked in a baseunit of measure into the product unit of measure (quantity in product unit of measure is rounded offto 3 decimal places) and back.In addition, for less than 3 rounding decimal places, the quantity in the product units of measuremay not have more decimal places than are determined by the rounding decimal places (quantity in

product unit of measure is not rounded off).For further details see section "One-to-one of the quantity conversion" further below.

Example 10: Examples for rounding decimals

The base unit of measure of a material is KG. Furthermore, the product unitsof measure PCS is used. You should make sure that the moved quantities always correspond to thecomplete piece.

You determine the number of rounding decimals per piece with 0.

For a batch with the piece weight 300 KG/PCS, a goods issue of more than 2800KG (corresponds to 9.333 PCS) can no longer be posted; depending on the situation, an error messageis generated or an error-free quantity (here: 2700 KG) is proposed.

d) Displayability of the conversion factor as a five-digit fraction

The conversion factor should always be one-to-one in a five-digit fraction.

This is at least always the case when the conversion factors have

a maximum of 5 places other than zero in sequence (significant places)



and

a maximum of 5 predecimal or 4 decimal places.

Conversion factors with more than 5 predecimal places can never berepresented as a five-digit fraction (largest value = 99999/1 ).

In additon, there are more conversion factors that are displayable as five-digit fraction, however they do not fulfill these conditions. Nevertheless, this simple rule can beused as a criteria that corresponds to the format listed above without having to conduct anothercheck (for example, from an external system).

Example 11:

Con.factor Significant places Pred.places Dec.places OK

12345.000 5 5 0 Yes 123456.000 6 6 0 No

1.1234 5 1 4 Yes 0.12345 5 0 5 ?

654,321 6 3 3 ?

Conversion factors which do not correspond to the conditions listed above should be adjusted througha function module. This must occur in relation to the the classification. For this, the ABAPfunctions CONVERT_TO_FRACT5 or MURC_ROUND_FOR_FRACT must be included in a variant function.

As a result, these functions return a divisor-foreign quotient whichcorresponds to the original conversion factor as exactly as possible. The difference between the two

functions is that the MURC_ROUND_FOR_FRACT always returns quotients which correspond to a finitedecimal fraction, whereas the CONVERT_TO_FRACT5 can find a better approach, however, which generallyresults in a cyclic (and thus no finite) decimal fraction.

An approach with the MURC_ROUND_FOR_FRACT must always occur exactly, if aunit of measure is in the denominator of the conversion factor which has less than 3 roundingdecimal places or is the base unit of measure and which should be posted in multiples of 10 ** (-<Number of the rounding decimal places>): A classic example of this are all (countable) units ofmeasure in whole numbers. Furthermore, the unit of measure in the numerator must be the base unit ofmeasure, or a product unit of measure with less than 3 rounding decimal places.

For product units of measure with 3 rounding decimal places, you can suppressthe check to the displayability of the decimal conversion factor as a five-digit numerator anddenominator through Note 435144.

Remark: All five-digit numerators and denominators can be mapped one-to-one to 15-digit decimal fractions.

This means that not the display of conversion factors as maximally 15-digit decimal fractionsrestricts the accuracy of quantity conversions but the number of places of denominators andnumerators.

e) One-to-one of the quantity conversion

The one-to-one of the quantity conversion means that the conversion of aquantity into another unit of measure and the calculation back into the original unit of measuredeliver the same result. This is checked during the conversion of product units of measure into thebase unit of measure. If the one-to-one is not given, the system will issue message XU056.

If the specification of the base unit of measure, the rounding decimal placesfor the product units of measure and the format of the conversion factors were adjusted correctlyand if the quantity is a multiple of the increment, then this message should not appear (for thecalculation of the increment, see function module documentation for the ABAP functions MURC_GCD andMURC_QUANTITY_CHECK or Note 519561).

You can restrict this check to a certain unit of measure with a BAdI (seeNote 612945).

f) The definition of the conversion factor is converted as a relationship from the base unitof measure for product unit of measure or vice versa.

The examples assume that the conversion factor is defined as the "ratio baseunit of measure to product unit of measure".

If the base unit of measure and the product unit of measure have the sameamount of rounding decimal places (particularly those that are whole numbers), then you shoulddivide the smaller unit of measure into the numerator (for example, piece/cardboard box).

If the product unit of measure has less than 3 rounding decimal places, andthe number of the rounding decimal places differs from the base unit of measure, then you shoulddivide the unit of measure that has fewer rounding decimal places into the denominator (for example,KG/PCS).

If the product unit of measure with 3 rounding decimal places is defined,then it is not important around how much the quotient is defined.

3. Using dependency and variant functions for setting conversion factors in classification



The dependency assigned to a batch class is always used when an object is classifiedin the batch class.

Maintenance of a plan conversion factor in the portion/product quantity view of thematerial master technically also corresponds to a classification of object MARM_WS. For this reason,the plan conversion factor you entered manually should not be set via dependency at the same time.Otherwise, message LB 109 may be displayed, and the entered plan conversion factor cannot be saved.

In variant functions, you can use function module CUDB_GET_TYPE to determine theobject type of the currently classified object via the ITYPE. Make sure that no dependency settingthe conversion factor is used for object type MARM_WS.

Validity

Correction Instructions

Support Packages & Patches

References

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SAP Notes

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SAP Notes (14)

Software Component From Rel. To Rel. And Subsequent

SAP_APPL 40A 40B

45A 45B

46A 46B

46C 46C

470 470

500 500

600 600

IS-MP 10B 10B

Correction Instructions

Software Component Valid from Valid to Number

SAP_APPL 45B 46B 234481

Support Packages

Software Component Release Support Package

IS-MP 10B SAPKIYM117

1853028 Fixing unit of measure conversion factor handling

1112075 Simple discontinuation: incorrect qty follow-up materl w/ATP

842624 MURC_REPLACE_ERFME prod unit w/o grid spacing for quantities

680228 Conversion error because char f conversion factor too short

672722 BADI MURC_REPLACE_ERFME considers lock tables 620775 XU056: Enhancement for BAdI for the unambiguity check

612945 XU056: BAdI for fine-tuned control of the one-to-one check

523496 FAQ: Alternative units of measure

519561 Default values for prod. Quant.: Error XU020 or too large

482411 Quantity conversion with product quantities - rounding error

435144 XU033 during conversion with product units of measure

391710 Rounding of characteristic values for quantity conversion

316229 Workaround:XU033 in goods mvt w. product quantities

122471 Conversion of unit of measure for goods movements

77525 Quantity unit conversion in inventory management

23771 Quantity conversion with non-metric units

1112075 Simple discontinuation: incorrect qty follow-up materl w/ATP

620775 XU056: Enhancement for BAdI for the unambiguity check

612945 XU056: BAdI for fine-tuned control of the one-to-one check

523496 FAQ: Alternative units of measure

519561 Default values for prod. Quant.: Error XU020 or too large



1853028 Fixing unit of measure conversion factor handling

680228 Conversion error because char f conversion factor too short

482411 Quantity conversion with product quantities - rounding error

435144 XU033 during conversion with product units of measure

316229 Workaround:XU033 in goods mvt w. product quantities

77525 Quantity unit conversion in inventory management

391710 Rounding of characteristic values for quantity conversion

23771 Quantity conversion with non-metric units

122471 Conversion of unit of measure for goods movements

base unit of measure ins

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