Handbook 44 – 2013 Appendix A – Fundamental Considerations

A-1 

Table of Contents

Appendix A. Fundamental Considerations Associated with the Enforcement of 

Handbook 44 Codes ............................................................................................ 3

1. Uniformity of Requirements........................................................................................................ 3

1.1. National Conference Codes............................................................................................................ 3

1.2. Form of Promulgation. ................................................................................................................... 3

2. Tolerances for Commercial Equipment ..................................................................................... 4

2.1. Acceptance and Maintenance Tolerances....................................................................................... 4

2.2. Theory of Tolerances...................................................................................................................... 4

2.3. Tolerances and Adjustments........................................................................................................... 4

3. Testing Apparatus........................................................................................................................ 4

3.1. Adequacy........................................................................................................................................ 4

3.2. Tolerances for Standards. ............................................................................................................... 4

3.3. Accuracy of Standards.................................................................................................................... 5

4. Inspection of Commercial Equipment........................................................................................ 5

4.1. Inspection Versus Testing .............................................................................................................. 5 

4.2. Necessity for Inspection. ................................................................................................................ 5

4.3. Specification Requirements............................................................................................................ 5

4.4 General Considerations .................................................................................................................. 6 

4.5. Misuse of Equipment...................................................................................................................... 6

4.6. Recommendations. ......................................................................................................................... 6

4.7. Accurate and Correct Equipment. .................................................................................................. 6

5. Correction of Commercial Equipment....................................................................................... 6

5.1. Adjustable Elements....................................................................................................................... 6

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

5.3. Gauging. ......................................................................................................................................... 7

6. Rejection of Commercial Equipment.......................................................................................... 7

6.1. Rejection and Condemnation ......................................................................................................... 7

7. Tagging of Equipment.................................................................................................................. 8

7.1. Rejected and Condemned............................................................................................................... 8

7.2. Nonsealed and Noncommercial...................................................................................................... 8

8. Records of Equipment.................................................................................................................. 8

9. Sealing of Equipment................................................................................................................... 9

9.1. Types of Seals and Their Locations. .............................................................................................. 9

9.2. Exceptions. ..................................................................................................................................... 9

10. Rounding Off Numerical Values................................................................................................. 9

10.1. Definition. ...................................................................................................................................... 9

10.2. General Rules. ................................................................................................................................ 9

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

10.4. Rules for Common Fractions........................................................................................................10
Appendix A – Fundamental Considerations Handbook 44 – 2013

A-2 

THIS PAGE INTENTIONALLY LEFT BLANK
Handbook 44 – 2013 Appendix A – Fundamental Considerations

A-3 

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).
Appendix A – Fundamental Considerations Handbook 44 – 2013

A-4 

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.

 

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 

Weights and Measures Division 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.
Handbook 44 – 2013 Appendix A – Fundamental Considerations

A-5 

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 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 
Appendix A – Fundamental Considerations Handbook 44 – 2013

A-6 

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.

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 

 

3 See Section 1.10. General Code and Appendix D. Definitions.
Handbook 44 – 2013 Appendix A – Fundamental Considerations

A-7 

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.

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 
Appendix A – Fundamental Considerations Handbook 44 – 2013

A-8 

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 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.
Handbook 44 – 2013 Appendix A – Fundamental Considerations

A-9 

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 

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.
Appendix A – Fundamental Considerations Handbook 44 – 2013

A-10

(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.

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.)
Handbook 44 – 2013 Appendix A – Fundamental Considerations

A-11

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.)
Appendix A – Fundamental Considerations Handbook 44 – 2013

A-12

THIS PAGE INTENTIONALLY LEFT BLANK