Handbook 44 – 2018 Appendix A – Fundamental Considerations

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Table of Contents

Appendix A. Fundamental Considerations Associated with the Enforcement of 

Handbook 44 Codes........................................................................................ A-3

1. Uniformity of Requirements.................................................................................................................... A-3

1.1. National Conference Codes....................................................................................................... A-3

1.2. Form of Promulgation. .............................................................................................................. A-3

2. Tolerances for Commercial Equipment ................................................................................................. A-4

2.1. Acceptance and Maintenance Tolerances.................................................................................. A-4

2.2. Theory of Tolerances................................................................................................................. A-4

2.3. Tolerances and Adjustments...................................................................................................... A-4

3. Testing Apparatus.................................................................................................................................... A-4

3.1. Adequacy................................................................................................................................... A-4

3.2. Tolerances for Standards. .......................................................................................................... A-4

3.3. Accuracy of Standards............................................................................................................... A-5

4. Inspection of Commercial Equipment.................................................................................................... A-5

4.1. Inspection Versus Testing. ........................................................................................................ A-5

4.2. Necessity for Inspection. ........................................................................................................... A-5

4.3. Specification Requirements....................................................................................................... A-5

4.4. General Considerations. ............................................................................................................ A-6

4.5. Misuse of Equipment................................................................................................................. A-6

4.6. Recommendations. .................................................................................................................... A-6

4.7. Accurate and Correct Equipment. ............................................................................................. A-6

5. Correction of Commercial Equipment................................................................................................... A-6

5.1. Adjustable Elements.................................................................................................................. A-6

5.2. When Corrections Should Be Made. ......................................................................................... A-7

5.3. Gauging. .................................................................................................................................... A-7

6. Rejection of Commercial Equipment ..................................................................................................... A-7

6.1. Rejection and Condemnation .................................................................................................... A-7

7. Tagging of Equipment.............................................................................................................................. A-8

7.1. Rejected and Condemned.......................................................................................................... A-8

7.2. Nonsealed and Noncommercial................................................................................................. A-8

8. Records of Equipment.............................................................................................................................. A-8

9. Sealing of Equipment............................................................................................................................... A-8

9.1. Types of Seals and Their Locations. ......................................................................................... A-8

9.2. Exceptions. ................................................................................................................................ A-9

10. Rounding Off Numerical Values............................................................................................................. A-9

10.1. Definition. ................................................................................................................................. A-9

10.2. General Rules. ........................................................................................................................... A-9

10.3. Rules for Reading of Indications............................................................................................. A-10

10.4. Rules for Common Fractions................................................................................................... A-10
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Appendix A. Fundamental Considerations Associated with the Enforcement 

of Handbook 44 Codes

1. Uniformity of Requirements

1.1. National Conference Codes. – Weights and measures jurisdictions are urged to promulgate and adhere to the 

National Conference codes, to the end that uniform requirements may be in force throughout the country. This action 

is recommended even though a particular jurisdiction does not wholly agree with every detail of the National 

Conference codes. Uniformity of specifications and tolerances is an important factor in the manufacture of 

commercial equipment. Deviations from standard designs to meet the special demands of individual weights and 

measures jurisdictions are expensive, and any increase in costs of manufacture is, of course, passed on to the purchaser 

of equipment. On the other hand, if designs can be standardized by the manufacturer to conform to a single set of 

technical requirements, production costs can be kept down, to the ultimate advantage of the general public. Moreover, 

it seems entirely logical that equipment that is suitable for commercial use in the “specification” states should be 

equally suitable for such use in other states.

Another consideration supporting the recommendation for uniformity of requirements among weights and measures 

jurisdictions is the cumulative and regenerative effect of the widespread enforcement of a single standard of design 

and performance. The enforcement effort in each jurisdiction can then reinforce the enforcement effort in all other 

jurisdictions. More effective regulatory control can be realized with less individual effort under a system of uniform 

requirements than under a system in which even minor deviations from standard practice are introduced by 

independent state action.

Since the National Conference codes represent the majority opinion of a large and representative group of experienced 

regulatory officials, and since these codes are recognized by equipment manufacturers as their basic guide in the 

design and construction of commercial weighing and measuring equipment, the acceptance and promulgation of these 

codes by each state are strongly recommended.

1.2. Form of Promulgation. – A convenient and very effective form of promulgation already successfully used in 

a considerable number of states is promulgation by citation of National Institute of Standards and Technology 

Handbook 44. It is especially helpful when the citation is so made that, as amendments are adopted from time to time 

by the National Conference on Weights and Measures, these automatically go into effect in the state regulatory 

authority. For example, the following form of promulgation has been used successfully and is recommended for 

consideration:

The specifications, tolerances, and other technical requirements for weighing and measuring devices as 

recommended by the National Conference on Weights and Measures and published in the National Institute of 

Standards and Technology Handbook 44, “Specifications, Tolerances, and Other Technical Requirements for 

Weighing and Measuring Devices,” and supplements thereto or revisions thereof, shall apply to commercial 

weighing and measuring devices in the state.

In some states, it is preferred to base technical requirements upon specific action of the state legislature rather than 

upon an act of promulgation by a state officer. The advantages cited above may be obtained and may yet be surrounded 

by adequate safeguards to insure proper freedom of action by the state enforcing officer if the legislature adopts the 

National Conference requirements by language somewhat as follows:

The specifications, tolerances, and other technical requirements for weighing and measuring devices as 

recommended by the National Conference on Weights and Measures shall be the specifications, tolerances, and 

other technical requirements for weighing and measuring devices of the state except insofar as specifically 

modified, amended, or rejected by a regulation issued by the state (insert title of enforcing officer).
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2. Tolerances for Commercial Equipment

2.1. Acceptance and Maintenance Tolerances. – The official tolerances prescribed by a weights and measures 

jurisdiction for commercial equipment are the limits of inaccuracy officially permissible within that jurisdiction. It is 

recognized that errorless value or performance of mechanical equipment is unattainable. Tolerances are established, 

therefore, to fix the range of inaccuracy within which equipment will be officially approved for commercial use. In 

the case of classes of equipment on which the magnitude of the errors of value or performance may be expected to 

change as a result of use, two sets of tolerances are established: acceptance tolerances and maintenance tolerances.

Acceptance tolerances are applied to new or newly reconditioned or adjusted equipment, and are smaller than (usually 

one-half of) the maintenance tolerances. Maintenance tolerances thus provide an additional range of inaccuracy within 

which equipment will be approved on subsequent tests, permitting a limited amount of deterioration before the 

equipment will be officially rejected for inaccuracy and before reconditioning or adjustment will be required. In 

effect, there is assured a reasonable period of use for equipment after it is placed in service before reconditioning will 

be officially required. The foregoing comments do not apply, of course, when only a single set of tolerance values is 

established, as is the case with equipment such as glass milk bottles and graduates, which maintain their original 

accuracy regardless of use, and measure-containers, which are used only once.

2.2. Theory of Tolerances. – Tolerance values are so fixed that the permissible errors are sufficiently small that 

there is no serious injury to either the buyer or the seller of commodities, yet not so small as to make manufacturing 

or maintenance costs of equipment disproportionately high. Obviously, the manufacturer must know what tolerances 

his equipment is required to meet, so that he can manufacture economically. His equipment must be good enough to 

satisfy commercial needs, but should not be subject to such stringent tolerance values as to make it unreasonably 

costly, complicated, or delicate.

2.3. Tolerances and Adjustments. – Tolerances are primarily accuracy criteria for use by the regulatory official. 

However, when equipment is being adjusted for accuracy, either initially or following repair or official rejection, the 

objective should be to adjust as closely as practicable to zero error. Equipment owners should not take advantage of 

tolerances by deliberately adjusting their equipment to have a value, or to give performance, at or close to the tolerance 

limit. Nor should the repair or service personnel bring equipment merely within tolerance range when it is possible 

to adjust closer to zero error.1

3. Testing Apparatus

3.1. Adequacy.2 – Tests can be made properly only if, among other things, adequate testing apparatus is available. 

Testing apparatus may be considered adequate only when it is properly designed for its intended use, when it is so 

constructed that it will retain its characteristics for a reasonable period under conditions of normal use, when it is 

available in denominations appropriate for a proper determination of the value or performance of the commercial 

equipment under test, and when it is accurately calibrated.

3.2. Tolerances for Standards. – Except for work of relatively high precision, it is recommended that the accuracy 

of standards used in testing commercial weighing and measuring equipment be established and maintained so that the 

use of corrections is not necessary. When the standard is used without correction, its combined error and uncertainty 

must be less than one-third of the applicable device tolerance.

Device testing is complicated to some degree when corrections to standards are applied. When using a correction for 

a standard, the uncertainty associated with the corrected value must be less than one-third of the applicable device 

 1 See General Code, Section 1.10.; User Requirement G-UR.4.3. Use of Adjustments.

2 Recommendations regarding the specifications and tolerances for suitable field standards may be obtained from the 

Office of Weights and Measures of the National Institute of Standards and Technology. Standards will meet the 

specifications of the National Institute of Standards and Technology Handbook 105-Series standards (or other 

suitable and designated standards). This section shall not preclude the use of additional field standards and/or 

equipment, as approved by the Director, for uniform evaluation of device performance.
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tolerance. The reason for this requirement is to give the device being tested as nearly as practicable the full benefit of 

its own tolerance.

3.3. Accuracy of Standards. – Prior to the official use of testing apparatus, its accuracy should invariably be 

verified. Field standards should be calibrated as often as circumstances require. By their nature, metal volumetric 

field standards are more susceptible to damage in handling than are standards of some other types. A field standard 

should be calibrated whenever damage is known or suspected to have occurred or significant repairs have been made. 

In addition, field standards, particularly volumetric standards, should be calibrated with sufficient frequency to affirm 

their continued accuracy, so that the official may always be in an unassailable position with respect to the accuracy of 

his testing apparatus. Secondary field standards, such as special fabric testing tapes, should be verified much more 

frequently than such basic standards as steel tapes or volumetric provers to demonstrate their constancy of value or 

performance.

Accurate and dependable results cannot be obtained with faulty or inadequate field standards. If either the service 

person or official is poorly equipped, their results cannot be expected to check consistently. Disagreements can be 

avoided and the servicing of commercial equipment can be expedited and improved if service persons and officials 

give equal attention to the adequacy and maintenance of their testing apparatus.

4. Inspection of Commercial Equipment

4.1. Inspection Versus Testing. – A distinction may be made between the inspection and the testing of commercial 

equipment that should be useful in differentiating between the two principal groups of official requirements; 

i.e., specifications and performance requirements. Although the term inspection is frequently loosely used to include 

everything that the official has to do in connection with commercial equipment, it is useful to limit the scope of that 

term primarily to examinations made to determine compliance with design, maintenance, and user requirements. The 

term testing may then be limited to those operations carried out to determine the accuracy of value or performance of 

the equipment under examination by comparison with the actual physical standards of the official. These two terms 

will be used herein in the limited senses defined.

4.2. Necessity for Inspection. – It is not enough merely to determine that the errors of equipment do not exceed the 

appropriate tolerances. Specification and user requirements are as important as tolerance requirements and should be 

enforced. Inspection is particularly important, and should be carried out with unusual thoroughness whenever the 

official examines a type of equipment not previously encountered.

This is the way the official learns whether or not the design and construction of the device conform to the specification 

requirements. But even a device of a type with which the official is thoroughly familiar and that he has previously 

found to meet specification requirements should not be accepted entirely on faith. Some part may have become 

damaged, or some detail of design may have been changed by the manufacturer, or the owner or operator may have 

removed an essential element or made an objectionable addition. Such conditions may be learned only by inspection. 

Some degree of inspection is therefore an essential part of the official examination of every piece of weighing or 

measuring equipment.

4.3. Specification Requirements. – A thorough knowledge by the official of the specification requirements is a 

prerequisite to competent inspection of equipment. The inexperienced official should have his specifications before 

him when making an inspection, and should check the requirements one by one against the equipment itself. 

Otherwise some important requirement may be overlooked. As experience is gained, the official will become 

progressively less dependent on the handbook, until finally observance of faulty conditions becomes almost automatic 

and the time and effort required to do the inspecting are reduced to a minimum. The printed specifications, however, 

should always be available for reference to refresh the official’s memory or to be displayed to support his decisions, 

and they are an essential item of his kit.

Specification requirements for a particular class of equipment are not all to be found in the separate code for that class. 

The requirements of the General Code apply, in general, to all classes of equipment, and these must always be 

considered in combination with the requirements of the appropriate separate code to arrive at the total of the 

requirements applicable to a piece of commercial equipment.
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4.4. General Considerations. – The simpler the commercial device, the fewer are the specification requirements 

affecting it, and the more easily and quickly can adequate inspection be made. As mechanical complexity increases, 

however, inspection becomes increasingly important and more time consuming, because the opportunities for the 

existence of faulty conditions are multiplied. It is on the relatively complex device, too, that the official must be on 

the alert to discover any modification that may have been made by an operator that might adversely affect the proper 

functioning of the device.

It is essential for the officials to familiarize themselves with the design and operating characteristics of the devices 

that he inspects and tests. Such knowledge can be obtained from the catalogs and advertising literature of device 

manufacturers, from trained service persons and plant engineers, from observation of the operations performed by 

service persons when reconditioning equipment in the field, and from a study of the devices themselves.

Inspection should include any auxiliary equipment and general conditions external to the device that may affect its 

performance characteristics. In order to prolong the life of the equipment and forestall rejection, inspection should 

also include observation of the general maintenance of the device and of the proper functioning of all required 

elements. The official should look for worn or weakened mechanical parts, leaks in volumetric equipment, or elements 

in need of cleaning.

4.5. Misuse of Equipment. – Inspection, coupled with judicious inquiry, will sometimes disclose that equipment 

is being improperly used, either through ignorance of the proper method of operation or because some other method 

is preferred by the operator. Equipment should be operated only in the manner that is obviously indicated by its 

construction or that is indicated by instructions on the equipment, and operation in any other manner should be 

prohibited.

4.6. Recommendations. – A comprehensive knowledge of each installation will enable the official to make 

constructive recommendations to the equipment owner regarding proper maintenance of his weighing and measuring 

devices and the suitability of his equipment for the purposes for which it is being used or for which it is proposed that 

it be used. Such recommendations are always in order and may be very helpful to an owner. The official will, of 

course, carefully avoid partiality toward or against equipment of specific makes, and will confine his recommendations 

to points upon which he is qualified, by knowledge and experience, to make suggestions of practical merit.

4.7. Accurate and Correct Equipment. – Finally, the weights and measures official is reminded that commercial 

equipment may be accurate without being correct. A piece of equipment is accurate when its performance or value 

(that is, its indications, its deliveries, its recorded representations, or its capacity or actual value, etc., as determined

by tests made with suitable standards) conforms to the standard within the applicable tolerances and other performance 

requirements. Equipment that fails so to conform is inaccurate. A piece of equipment is correct when, in addition to 

being accurate, it meets all applicable specification requirements. Equipment that fails to meet any of the requirements 

for correct equipment is incorrect. Only equipment that is correct should be sealed and approved for commercial use.3

5. Correction of Commercial Equipment

5.1. Adjustable Elements. – Many types of weighing and measuring instruments are not susceptible to adjustment 

for accuracy by means of adjustable elements. Linear measures, liquid measures, graduates, measure-containers, milk 

and lubricating-oil bottles, farm milk tanks, dry measures, and some of the more simple types of scales are in this 

category. Other types (for example, taximeters and odometers and some metering devices) may be adjusted in the 

field, but only by changing certain parts such as gears in gear trains.

Some types, of which fabric-measuring devices and cordage-measuring devices are examples, are not intended to be 

adjusted in the field and require reconditioning in shop or factory if inaccurate. Liquid-measuring devices and most 

scales are equipped with adjustable elements, and some vehicle-tank compartments have adjustable indicators. Field 

adjustments may readily be made on such equipment. In the discussion that follows, the principles pointed out and 

the recommendations made apply to adjustments on any commercial equipment, by whatever means accomplished.

 3 See Section 1.10. General Code and Appendix D. Definitions.
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5.2. When Corrections Should Be Made. – One of the primary duties of a weights and measures official is to 

determine whether equipment is suitable for commercial use. If a device conforms to all legal requirements, the 

official “marks” or “seals” it to indicate approval. If it does not conform to all official requirements, the official is 

required to take action to ensure that the device is corrected within a reasonable period of time. Devices with 

performance errors that could result in serious economic injury to either party in a transaction should be prohibited 

from use immediately and not allowed to be returned to service until necessary corrections have been made. The 

official should consider the most appropriate action, based on all available information and economic factors.

Some officials contend that it is justifiable for the official to make minor corrections and adjustments if there is no 

service agency nearby or if the owner or operator depends on this single device and would be “out of business” if the 

use of the device were prohibited until repairs could be made. Before adjustments are made at the request of the owner 

or the owner’s representative, the official should be confident that the problem is not due to faulty installation or a 

defective part, and that the adjustment will correct the problem. The official should never undertake major repairs, or 

even minor corrections, if services of commercial agencies are readily available. The official should always be 

mindful of conflicts of interest before attempting to perform any services other than normal device examination and 

testing duties.

(Amended 1995)

5.3. Gauging. – In the majority of cases, when the weights and measures official tests commercial equipment, he 

is verifying the accuracy of a value or the accuracy of the performance as previously established either by himself or 

by someone else. There are times, however, when the test of the official is the initial test on the basis of which the 

calibration of the device is first determined or its performance first established. The most common example of such 

gauging is in connection with vehicle tanks the compartments of which are used as measures. Frequently the official 

makes the first determination on the capacities of the compartments of a vehicle tank, and his test results are used to 

determine the proper settings of the compartment indicators for the exact compartment capacities desired. 

Adjustments of the position of an indicator under these circumstances are clearly not the kind of adjustments discussed 

in the preceding paragraph.

6. Rejection of Commercial Equipment

6.1. Rejection and Condemnation. – The Uniform Weights and Measures Law contains a provision stating that 

the director shall reject and order to be corrected such physical weights and measures or devices found to be incorrect. 

Weights and measures and devices that have been rejected, may be seized if not corrected within a reasonable time or 

if used or disposed of in a manner not specifically authorized. The director shall remove from service and may seize 

weights and measures found to be incorrect that are not capable of being made correct.

These broad powers should be used by the official with discretion. The director should always keep in mind the 

property rights of an equipment owner, and cooperate in working out arrangements whereby an owner can realize at 

least something from equipment that has been rejected. In cases of doubt, the official should initially reject rather 

than condemn outright. Destruction and confiscation of equipment are harsh procedures. Power to seize and destroy 

is necessary for adequate control of extreme situations, but seizure and destruction should be resorted to only when 

clearly justified.

On the other hand, rejection is clearly inappropriate for many items of measuring equipment. This is true for most 

linear measures, many liquid and dry measures, graduates, measure-containers, milk bottles, lubricating-oil bottles, 

and some scales. When such equipment is “incorrect,” it is either impractical or impossible to adjust or repair it, and 

the official has no alternative to outright condemnation. When only a few such items are involved, immediate 

destruction or confiscation is probably the best procedure. If a considerable number of items are involved (as, for 

example, a stock of measures in the hands of a dealer or a large shipment of bottles), return of these to the manufacturer 

for credit or replacement should ordinarily be permitted provided that the official is assured that they will not get into 

commercial use. In rare instances, confiscation and destruction are justified as a method of control when less harsh 

methods have failed.

In the case of incorrect mechanisms such as fabric-measuring devices, taximeters, liquid-measuring devices, and most 

scales, repair of the equipment is usually possible, so rejection is the customary procedure. Seizure may occasionally 
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be justified, but in the large majority of instances this should be unnecessary. Even in the case of worn-out equipment, 

some salvage is usually possible, and this should be permitted under proper controls.

(Amended 1995)

7. Tagging of Equipment

7.1. Rejected and Condemned. – It will ordinarily be practicable to tag or mark as rejected each item of equipment 

found to be incorrect and considered susceptible of proper reconditioning. However, it can be considered justifiable 

not to mark as rejected incorrect devices capable of meeting acceptable performance requirements if they are to be 

allowed to remain in service for a reasonable time until minor problems are corrected since marks of rejection may 

tend to be misleading about a device’s ability to produce accurate measurements during the correction period. The 

tagging of equipment as condemned, or with a similar label to indicate that it is permanently out of service, is not 

recommended if there is any other way in which the equipment can definitely be put out of service. Equipment that 

cannot successfully be repaired should be dismantled, removed from the premises, or confiscated by the official rather 

than merely being tagged as “condemned.”

(Amended 1995)

7.2. Nonsealed and Noncommercial. – Rejection is not appropriate if measuring equipment cannot be tested by 

the official at the time of his regular visit–for example, when there is no gasoline in the supply tank of a 

gasoline-dispensing device. Some officials affix to such equipment a nonsealed tag stating that the device has not 

been tested and sealed and that it must not be used commercially until it has been officially tested and approved. This 

is recommended whenever considerable time will elapse before the device can be tested.

Where the official finds in the same establishment, equipment that is in commercial use and also equipment suitable 

for commercial use that is not presently in service, but which may be put into service at some future time, he may treat 

the latter equipment in any of the following ways:

(a) Test and approve the same as commercial equipment in use.

(b) Refrain from testing it and remove it from the premises to preclude its use for commercial purposes.

(c) Mark the equipment nonsealed.

Where the official finds commercial equipment and noncommercial equipment installed or used in close proximity, 

he may treat the noncommercial equipment in any of the following ways:

(a) Test and approve the same as commercial equipment.

(b) Physically separate the two groups of equipment so that misuse of the noncommercial equipment will be 

prevented.

(c) Tag it to show that it has not been officially tested and is not to be used commercially.

8. Records of Equipment

8.1. The official will be well advised to keep careful records of equipment that is rejected, so that he may follow up 

to insure that the necessary repairs have been made. As soon as practicable following completion of repairs, the 

equipment should be retested. Complete records should also be kept of equipment that has been tagged as nonsealed 

or noncommercial. Such records may be invaluable should it subsequently become necessary to take disciplinary 

steps because of improper use of such equipment.

9. Sealing of Equipment

9.1. Types of Seals and Their Locations. – Most weights and measures jurisdictions require that all equipment 

officially approved for commercial use (with certain exceptions to be pointed out later) be suitably marked or sealed 
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to show approval. This is done primarily for the benefit of the public to show that such equipment has been officially 

examined and approved. The seal of approval should be as conspicuous as circumstances permit and should be of 

such a character and so applied that it will be reasonably permanent. Uniformity of position of the seal on similar 

types of equipment is also desirable as a further aid to the public.

The official will need more than one form of seal to meet the requirements of different kinds of equipment. Good 

quality, weather-resistant, water-adhesive, or pressure-sensitive seals or decalcomania seals are recommended for 

fabric-measuring devices, liquid-measuring devices, taximeters, and most scales, because of their permanence and 

good appearance. Steel stamps are most suitable for liquid and dry measures, for some types of linear measures, and 

for weights. An etched seal, applied with suitable etching ink, is excellent for steel tapes, and greatly preferable to a 

seal applied with a steel stamp. The only practicable seal for a graduate is one marked with a diamond or carbide 

pencil, or one etched with glass-marking ink. For a vehicle tank, the official may wish to devise a relatively large 

seal, perhaps of metal, with provision for stamping data relative to compartment capacities, the whole to be welded or 

otherwise permanently attached to the shell of the tank. In general, the lead-and-wire seal is not suitable as an approval 

seal.

9.2. Exceptions. – Commercial equipment such as measure-containers, milk bottles, and lubricating-oil bottles are 

not tested individually because of the time element involved. Because manufacturing processes for these items are 

closely controlled, an essentially uniform product is produced by each manufacturer. The official normally tests 

samples of these items prior to their sale within his jurisdiction and subsequently makes spot checks by testing samples 

selected at random from new stocks.

Another exception to the general rule for sealing approved equipment is found in certain very small weights whose 

size precludes satisfactory stamping with a steel die.

10. Rounding Off Numerical Values

10.1. Definition. – To round off or round a numerical value is to change the value of recorded digits to some other 

value considered more desirable for the purpose at hand by dropping or changing certain figures. For example, if a 

computed, observed, or accumulated value is 4738, this can be rounded off to the nearest thousand, hundred, or ten, 

as desired. Such rounded-off values would be, respectively, 5000, 4700, and 4740. Similarly, a value such as 47.382 

can be rounded off to two decimal places, to one decimal place, or to the units place. The rounded-off figures in this 

example would be, respectively, 47.38, 47.4, and 47.

10.2. General Rules. – The general rules for rounding off may be stated briefly as follows:

(a) When the figure next beyond the last figure or place to be retained is less than 5, the figure in the last place 

retained is to be kept unchanged. When rounding off 4738 to the nearest hundred, it is noted that the figure 3 

(next beyond the last figure to be retained) is less than 5. Thus the rounded-off value would be 4700. 

Likewise, 47.382 rounded to two decimal places becomes 47.38.

(b) When the figure next beyond the last figure or place to be retained is greater than 5, the figure in the last 

place retained is to be increased by 1. When rounding off 4738 to the nearest thousand, it is noted that the 

figure 7 (next beyond the last figure to be retained) is greater than 5. Thus the rounded-off value would 

be 5000. Likewise, 47.382 rounded to one decimal place becomes 47.4.

(c) When the figure next beyond the last figure to be retained is 5 followed by any figures other than zero(s), 

treat as in (b) above; that is, the figure in the last place retained is to be increased by 1. When rounding 

off 4501 to the nearest thousand, 1 is added to the thousands figure and the result becomes 5000.

(d) When the figure next beyond the last figure to be retained is 5 and there are no figures, or only zeros, beyond 

this 5, the figure in the last place to be retained is to be left unchanged if it is even (0, 2, 4, 6, or 8) and is to 

be increased by 1 if it is odd (1, 3, 5, 7, or 9). This is the odd and even rule, and may be stated as follows: 

“If odd, then add.” Thus, rounding off to the first decimal place, 47.25 would become 47.2 and 47.15 would 

become 47.2. Also, rounded to the nearest thousand, 4500 would become 4000 and 1500 would 

become 2000.
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It is important to remember that, when there are two or more figures to the right of the place where the last significant 

figure of the final result is to be, the entire series of such figures must be rounded off in one step and not in two or 

more successive rounding steps. [Expressed differently, when two or more such figures are involved, these are not to 

be rounded off individually, but are to be rounded off as a group.] Thus, when rounding off 47.3499 to the first 

decimal place, the result becomes 47.3. In arriving at this result, the figures “499” are treated as a group. Since 

the 4 next beyond the last figure to be retained is less than 5, the “499” is dropped (see subparagraph (a) above). It 

would be incorrect to round off these figures successively to the left so that 47.3499 would become 47.350 and 

then 47.35 and then 47.4.

10.3. Rules for Reading of Indications. – An important aspect of rounding off values is the application of these 

rules to the reading of indications of an indicator-and-graduated-scale combination (where the majority of the 

indications may be expected to lie somewhere between two graduations) if it is desired to read or record values only 

to the nearest graduation. Consider a vertical graduated scale and an indicator. Obviously, if the indicator is between 

two graduations but is closer to one graduation than it is to the other adjacent graduation, the value of the closer 

graduation is the one to be read or recorded.

In the case where, as nearly as can be determined, the indicator is midway between two graduations, the odd-and-even 

rule is invoked, and the value to be read or recorded is that of the graduation whose value is even. For example, if the 

indicator lies exactly midway between two graduations having values of 471 and 472, respectively, the indication 

should be read or recorded as 472, this being an even value. If midway between graduations having values of 474 

and 475, the even value 474 should be read or recorded. Similarly, if the two graduations involved had values of 470 

and 475, the even value of 470 should be read or recorded.

A special case not covered by the foregoing paragraph is that of a graduated scale in which successive graduations are 

numbered by twos, all graduations thus having even values; for example, 470, 472, 474, etc. When, in this case, an 

indication lies midway between two graduations, the recommended procedure is to depart from the practice of reading 

or recording only to the value of the nearest graduation and to read or record the intermediate odd value. For example, 

an indication midway between 470 and 472 should be read as 471.

10.4. Rules for Common Fractions. – When applying the rounding-off rules to common fractions, the principles 

are to be applied to the numerators of the fractions that have, if necessary, been reduced to a common denominator. 

The principle of “5s” is changed to the one-half principle; that is, add if more than one-half, drop if less than one-half, 

and apply the odd-and even rule if exactly one-half.

For example, a series of values might be 11

/32, 12/32, 13/32, 14/32, 15/32, 16/32, 17/32, 18/32, 19/32. Assume that these values are 

to be rounded off to the nearest eighth (4

/32). Then,

11

/32 becomes 1. (1/32 is less than half of 4/32 and accordingly is dropped.)

12

/32 becomes 1. (2/32 is exactly one-half of 4/32; it is dropped because it is rounded (down) to the “even” eighth, 

which in this instance is 0

/8.)

13

/32 becomes 14/32 or 11/8. (3/32 is more than half of 4/32, and accordingly is rounded “up” to 4/32 or 1/8).

14

/32 remains unchanged, being an exact eighth (11/8).

15

/32 becomes 14/32 or 11/8. (5/32 is 1/32 more than an exact 1/8; 1/32 is less than half of 4/32 and accordingly is dropped.)

16

/32 becomes 12/8 or 11⁄4. (6/32 is 2/32 more than an exact 1/8; 2/32 is exactly one-half of 4/32, and the final fraction is 

rounded (up) to the “even” eighth, which in this instance is 2

/8.)

17

/32 becomes 12/8 or 11⁄4. (7/32 is 3/32 more than an exact 1/8; 3/32 is more than one-half of 4/32 and accordingly the final 

fraction is rounded (up) to 2

/8 or 1⁄4.)

18

/32 remains unchanged, being an exact eighth (12/8 or 11⁄4.)

19

/32 becomes 12/8 or 11⁄4. (9/32 is 1/32 more than an exact 1/8; 1/32 is less than half of 4/32 and accordingly is dropped.)