RULE II--NUMERIC SIGNS AND SYMBOLS

• 0
  0

  	verbose	0

• 1
  1

  	verbose	1

• 2
  2

  	verbose	2

• 3
  3

  	verbose	3

• 4
  4

  	verbose	4

• 5
  5

  	verbose	5

• 6
  6

  	verbose	6

• 7
  7

  	verbose	7

• 8
  8

  	verbose	8

• 9
  9

  	verbose	9

• American
  ,

  	verbose	comma

• Continental
  ,

  	verbose	period

• American
  .

  	verbose	period

• Continental
  .

  	verbose	comma

§7. Representation of Arabic Numerals:

a. Digits are represented in two ways: as in English Braille, and as in Nemeth Code. The digits in English Braille are represented by the letters "j" and "a" through "i". The digits in the Nemeth Code are represented by the symbols whose configurations correspond to these same letters, but which occupy the lower portion of the braille cell.

b. Even when a work is transcribed in the Nemeth Code, when at all practical or appropriate, all numerals on title pages must be transcribed as in English Braille. Numerals at the corners of pages and at the ends of page-separation lines must also be transcribed as in English Braille. English Braille numerals must be used when the technique of "keying" (§187) is employed. In all other cases, including contents pages, forewords, page references, footnotes, indices, and bibliographies, the numerals of the Nemeth Code must be used.

§8. Comma, Decimal Point:

a. The transcriber should be alert to the possibility that variant forms of the comma and decimal point are sometimes employed, particularly in books published outside of the United States. Although the ink print signs for the comma and decimal point differ from

those used in the United States, this difference is not reflected in the braille transcription. However, a transcriber's note should be included at the beginning of the book to inform the reader of the continental usage in the ink-print edition.

(1)

#1,378

(American usage of comma)

verbose semantics

1,378

(2)

#1,378

(Continental usage of comma)

verbose semantics

1.378

(3)

#3.76

(American usage of decimal)

verbose semantics

3.76

(4)

#3.76

(Continental usage of decimal)

verbose semantics

3,76

b. The comma, American or Continental, which is interior to a numeral, and which is used to partition the numeral into short regular segments, must be regarded as a numeric symbol. As such, the comma is subject to the rules for transcribing numerals.

(1)

#1,478

(the comma is a numeric symbol, not a punctuation mark)

verbose semantics

1,478

(2)

#100, #200, #300

(the commas are punctuation marks, not numeric symbols)

verbose semantics

100 comma 200 comma 300

c. The decimal point, American or Continental, should be regarded as a numeric symbol only when it is associated with a numeral. An omission symbol must not be regarded as a numeric symbol. As a numeric symbol, the decimal point is subject to the rules for transcribing numerals.

(1)

#.35

(the decimal point is a numeric symbol)

verbose semantics

.35

(2)

#3.14

(the decimal point is a numeric symbol)

verbose semantics

3.14

(3)

#.2a1a2a3

(the decimal point is a numeric symbol)

verbose semantics

.2 a 1 a 2 a 3

(4)

."a1a2a3

(the decimal point is not a numeric symbol)

verbose semantics

period a 1 a 2 a 3

(5)

#.1+.2 .k ."----

(the first two decimal points are numeric symbols)

verbose semantics

.1 plus .2 equals period large-dash

§9. Use of the Numeric Indicator: The numeric indicator must be used to introduce one or more unspaced numeric symbols under the following circumstances:

a. The numeric indicator must be used at the beginning of a braille line or after a space. It must also be used after a minus symbol which occurs at the beginning of a braille line or which follows a space. For exceptions, see §11.

(1)

#27

verbose semantics

27

(2)

,"! 7 #7 balls4

verbose semantics

There were 7 balls period

(3)

#1+x+y .k #0

(1 plus x plus y equals 0)

verbose semantics

1 plus x plus y equals 0

(4)

y .k #2sin x

(y equals 2 sine x)

verbose semantics

y equals 2 sine x

(5)

sin #1

verbose semantics

sine 1

(6)

sin^2 #2x

(sine squared of 2x)

verbose semantics

sine squared 2 x

(7)

#0.333 ''' #3 '''

verbose semantics

0.333 ellipsis 3 ellipsis

(8)

log10 #2

verbose semantics

log Subscript 10 Baseline 2

(9)

$[ #1

(angle 1)

verbose semantics

angle 1

(10)

(x .k #0)

(x equals 0 enclosed in parentheses)

verbose semantics

left-parenthesis x equals 0 right-parenthesis

(11)

  #11  
?333#
  #5  

(a simple fraction)

verbose semantics

StartFraction 11 Over 5 EndFraction

(12)

   #1+3   
  ?3333#  
   #4+5   
,?333333,#
   #3+4   
  ?3333#  
   #5+6   

(a complex fraction)

verbose semantics

StartStartFraction StartFraction 1 plus 3 Over 4 plus 5 EndFraction OverOver StartFraction 3 plus 4 Over 5 plus 6 EndFraction EndEndFraction

(13)

           ;d         ;d           
     (1-x)?33#(2x)-2x?33#(1-x)     
           dx         dx           
   ,?3333333333333333333333333,#   
              (1-x)^2              
,,?33333333333333333333333333333,,#
                #2x                
           #1+(?3333#)^2           
                #1-x               

(a hypercomplex fraction)

verbose semantics

StartStartStartFraction StartStartFraction left-parenthesis 1 minus x right-parenthesis StartFraction d Over d x EndFraction left-parenthesis 2 x right-parenthesis minus 2 x StartFraction d Over d x EndFraction left-parenthesis 1 minus x right-parenthesis OverOver left-parenthesis 1 minus x right-parenthesis squared EndEndFraction OverOverOver 1 plus left-parenthesis StartFraction 2 x Over 1 minus x EndFraction right-parenthesis squared EndEndEndFraction

(14)

-#1

(minus 1)

verbose semantics

negative 1

(15)

-#.3

(minus three tenths)

verbose semantics

negative .3

b. The numeric indicator must be used after a punctuation mark. However, the hyphen requires special attention (see section f below). It must also be used after a minus symbol which follows a punctuation mark.

(1)

8#3 dogs0

verbose semantics

quote 3 dogs quote

(2)

,probabil;y--#0

verbose semantics

Probability large-dash 0

(3)

8#.5

verbose semantics

quote .5

(4)

8-#4

verbose semantics

quote negative 4

c. The numeric indicator must be used after a left grouping symbol which introduces a determinant or matrix. It must also be used after a minus symbol which follows such a grouping symbol.

(1)

,\#1  #2 ,\
,\-#3 -#4,\

verbose semantics

Start 2 By 2 Determinant 1st Row 1st Column 1 2nd Column 2 2nd Row 1st Column minus 3 2nd Column minus 4 EndDeterminant

(2)

,\#1    #1 ,\
,\     ?33#,\
,\      #2 ,\
,\         ,\
,\ #1   #1 ,\
,\?33# ?33#,\
,\ #2   #4 ,\

verbose semantics

Start 2 By 2 Determinant 1st Row 1 one-half 2nd Row one-half one-fourth EndDeterminant

d. The numeric indicator must be used after a section mark, paragraph mark, crosshatch, or asterisk. It must also be used after the general reference indicator or any reference symbol.

(1)

#3@,s#4

(3 section mark 4)

verbose semantics

3 section-mark 4

(2)

#3.##4

(3 crosshatch 4)

verbose semantics

3 Number-sign 4

(3)

#3@##4

(3 asterisk 4)

verbose semantics

3 asterisk 4

(4)

,see page #15 @]#"_4

(1 follows the general reference indicator; the 1 is raised in ink print)

verbose semantics

See page 15 Superscript 1 Baseline period

(5)

_]#3

(dagger 3)

verbose semantics

dagger 3

e. The numeric indicator must be used after any of the type-form indicators, or after making a transition from non-regular to regular type within the same numeral. It must also be used after the interior shape-modification indicator.

(1)

.#3

(italicized 3)

verbose semantics

Italic 3

(2)

_#0

(boldface zero)

verbose semantics

Bold 0

(3)

.#.3

(italicized three tenths)

verbose semantics

Italic .3

(4)

@#2

(script 2)

verbose semantics

Script .2

(5)

_#43#56

(the first two digits in boldface type, the last two in regular type)

verbose semantics

Bold 43 56

(6)

$c_$#5]

(5 enclosed within a circle)

verbose semantics

circled five

(7)

$4_$#5]

(5 enclosed within a square)

verbose semantics

square around 5

f. The numeric indicator must be used after a hyphen when the hyphen follows a word, an abbreviation, or a mark of punctuation. However, also see §11d.

(1)

#1-to-#1 correspond;e

verbose semantics

1 hyphen to hyphen 1 correspondence

(2)

hydrog5-#3

verbose semantics

hydrogen hyphen 3

(3)

,,dc-#7

verbose semantics

DC hyphen 7

(4)

;,b-#49 bomb]

verbose semantics

B hyphen 49 bomber

(5)

;,u-#238

verbose semantics

U hyphen 238

(6)

(287_8-#212 ,b4,c4)

verbose semantics

left-parenthesis 287 question-mark hyphen 212 B period C period right-parenthesis

g. The numeric indicator must be used after the opening transcriber's grouping symbol.

(1)

,9 x^2, ! #2 ,'#2 elevat$ 9
  pr9t,' is ! expon5t4

verbose semantics

In x squared comma the squared is the exponent period

§10. Definition of "Enclosed List":

An "enclosed list", for the purpose of this Code, must meet the following requirements:

(1)

#1, ;i, -#1, -i

(not an "enclosed list" according to i)

verbose semantics

1 comma i comma negative 1 comma negative i

(2)

(a, b@)

(an "enclosed list"; meets all requirements)

verbose semantics

left-parenthesis a comma b right-bracket

(3)

(?1/4#, ?1/2#+x, ?3/4#+x^2")

(an "enclosed list"; meets all requirements)

verbose semantics

left-parenthesis one-fourth comma one-half plus x comma three-fourths plus x squared right-parenthesis

(4)

(1, #2, & #3)

(not an "enclosed list" according to ii)

verbose semantics

left-parenthesis 1 comma 2 comma and 3 right-parenthesis

(5)

(;h ft1 ;k in)

(not an "enclosed list" according to ii)

verbose semantics

left-parenthesis h feet comma k inches right-parenthesis

(6)

(1st, #2nd, #3rd)

(not an "enclosed list" according to ii)

verbose semantics

left-parenthesis 1st comma 2nd comma 3rd right-parenthesis

(7)

(;x_'s, ;y_'s, ;z_'s,

(not an "enclosed list" according to ii)

verbose semantics

left-parenthesis x apostrophe s comma y apostrophe s comma z apostrophe s right-parenthesis

(8)

@($[ #1^.*, sin #1^.*"@)

(angle 1 degree, sine 1 degree; an "enclosed list"; meets all requirements)

verbose semantics

left-bracket angle 1 degree comma sine 1 degree right-bracket

(9)

(a, b, ''')

(an "enclosed list"; meets all requirements)

verbose semantics

left-parenthesis a comma b comma ellipsis right-parenthesis

(10)

(x+1, x+2, =, =, x+5)

(an "enclosed list"; meets all requirements)

verbose semantics

left-parenthesis x plus 1 comma x plus 2 comma question-mark comma question-mark comma x plus 5 right-parenthesis

(11)

(x .k #1, #2, ''', #10)

(not an "enclosed list" according to v)

verbose semantics

left-parenthesis x equals 1 comma 2 comma ellipsis comma 10 right-parenthesis

(12)

(a .k #1, b .k #2, c .k -#4)

(not an "enclosed list" according to v)

verbose semantics

left-parenthesis a equals 1 comma b equals 2 comma c equals negative 4 right-parenthesis

(13)

(;u, ;v_2 ;x, ;y)

(not an "enclosed list" according to vi)

verbose semantics

left-parenthesis u comma v semicolon x comma y right-parenthesis

(14)

(1 #2 #3)

(not an "enclosed list" according to vi)

verbose semantics

left-parenthesis 1 2 3 right-parenthesis

§11. Non-Use of the Numeric Indicator: It must not be assumed that because a symbol is numeric that the numeric indicator must be used with that symbol. The numeric indicator must not be used preceding a numeric symbol under the following circumstances:

a. The numeric indicator must not be used at the beginning of an item which is part of an "enclosed list" as defined in §10 above, even if such an item has been run over to another line. However, if any item in an "enclosed list" is a numeral in a type form other than regular type, that item requires the numeric indicator.

(1)

'(0, 1')

verbose semantics

left-bracket 0 comma 1 right-bracket

(2)

(-1, -2, -3)

verbose semantics

left-parenthesis negative 1 comma negative 2 comma negative 3 right-parenthesis

(3)

(1+h, 2+k, 0)

verbose semantics

left-parenthesis 1 plus h comma 2 plus k comma 0 right-parenthesis

(4)

(0, -1, +-2)

verbose semantics

left-parenthesis 0 comma minus 1 comma plus-or-minus 2 right-parenthesis

(5)

(2sin #30^.*, 3cos #60^.*")

(the numeric indicator is required before the 30 and the 60 because these are not the beginning of their respective items)

verbose semantics

left-parenthesis 2 sine 30 degree comma 3 cosine 60 degree right-parenthesis

(6)

(1, 2, 3, 4, 5, 6, 7, 8, 9,
   10, 11, 12)

(the numeric indicator is not required before 10 even though 10 begins a new line)

verbose semantics

StartLayout 1st Row left-parenthesis 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 2nd Row 10 comma 11 comma 12 right-parenthesis EndLayout

(7)

(x, 7, _#8, y)

(the 8 in this "enclosed list" is in boldface type)

verbose semantics

left-parenthesis x comma 7 comma 8 comma y right-parenthesis

b. The numeric indicator must not be used in work arranged in columns and aligned for addition, subtraction, multiplication, division, or alignment of a system of equations.

(1)

  273 
 + 85 
333333

(a problem aligned for addition)

verbose semantics

StartLayout 1st Row 273 2nd Row plus 85 EndLayout

(2)

  426 
 @*34 
333333

(a problem aligned for multiplication)

verbose semantics

StartLayout 1st Row 1st Column Blank 2nd Column 4 3rd Column 2 4th Column 6 2nd Row 1st Column times 2nd Column Blank 3rd Column 3 4th Column 4 EndLayout

(3)

    18 r"2 
  333333333
25o452     

(a problem aligned for division)

verbose semantics

MathSpeak can not yet render this equation period Please check back later period

(4)

2x- y- 5z+ 9 .k 0
   7y- 5z+28 .k 0
   5y-11z-43 .k 0

(alignment of three equations)

verbose semantics

StartLayout 1st Row 1st Column 2 x 2nd Column minus y 3rd Column minus 5 z 4th Column plus 9 5th Column equals 6th Column 0 2nd Row 1st Column Blank 2nd Column 7 y 3rd Column minus 5 z 4th Column plus 28 5th Column equals 6th Column 0 3rd Row 1st Column Blank 2nd Column 5 y 3rd Column minus 11 z 4th Column minus 43 5th Column equals 6th Column 0 EndLayout

c. The numeric indicator must not be used after a space if the purpose of the space is to partition a numeral into segments.

(1)

.p .k #3.14159 26535 '''

verbose semantics

pi equals 3.1415926535 ellipsis

(2)

#947,     147,   592
,millions ,?\s&s ,"os or ,units

verbose semantics

StartLayout 1st Row 1st Column 947 comma 2nd Column 147 comma 3rd Column 592 2nd Row 1st Column Millions 2nd Column Thousands 3rd Column Ones or Units EndLayout

d. The numeric indicator must not be used after a hyphen if the hyphen follows a numeral, a letter, or other mathematical expression.

(1)

#65-75

verbose semantics

65 minus 75

(2)

#3_3#30-4_3#45

(three thirty to four forty-five)

verbose semantics

3 colon 30 hyphen 4 colon 45

(3)

,r1d sec;n ;,'-12_4

verbose semantics

Read section A hyphen 12 period

e. The numeric indicator must not be used in any situation not covered in §§9 and 11.

(1)

x^2

verbose semantics

x squared

(2)

?3/x#

verbose semantics

StartFraction 3 Over x EndFraction

(3)

r"5

(remainder of 5 as in a division problem)

verbose semantics

r Baseline 5

(4)

ax^3"+bx^2"y+cxy^2"+dy^3"+ex^2"+y^2
   "-7

verbose semantics

a x cubed plus b x squared y plus c x y squared plus d y cubed plus e x squared plus y squared minus 7

(5)

x-5

verbose semantics

x minus 5

(6)

#2'*4

verbose semantics

2 times 4

(7)

#10,000

(in this numeral, the comma is not a punctuation mark)

verbose semantics

10,000

(8)

\-3\

(the absolute value of minus 3)

verbose semantics

StartAbsoluteValue negative 3 EndAbsoluteValue

§12. Long Numerals: Long numerals that cannot be completely accommodated on one braille line may be divided and run over to another line. Such a division must be made after a comma, if present, and a hyphen must be supplied. The numeric indicator must be used as the first braille symbol of the braille line to which the numeral has been run over.

(1)

#100,000,000,000,-
  #000

verbose semantics

StartLayout 1st Row 100,000,000,000 comma minus 2nd Row 000 EndLayout

(2)

#100000000000-
  #000

verbose semantics

StartLayout 1st Row 100000000000 minus 2nd Row 000 EndLayout

§13. Representation of Numerals to Non-Decimal Bases:

a. When a system of numeration is to a base other than 10, a common technique for providing additional digits is to use letters, either lower-case or capitalized, in addition to the ten Arabic digits. When this technique is used, the transcriber must use only lower-case letters. If capitalized letters are used in ink print, the transcriber must indicate this fact in a transcriber's note.

(1)

#13te7

(a base-12 numeral in which T represents 10 and E represents 11)

verbose semantics

Number 1 3 T E 7

(2)

#3ffe2

(a base-16 numeral in which E represents 14 and F represents 15)

verbose semantics

Number 3 F F E 2

b. Another common technique for providing additional digits is to use standard or arbitrary signs to supplement the ten Arabic digits. Authors sometimes give names to these signs. For example, &dek; (dek) represents 10 and ⪙ (el) represents 11. In this case, the transcriber must devise one-cell symbols for these signs, preferably chosen from among the letters of the English alphabet, and must insert a transcriber's note to specify the meanings which have been assigned to these symbols. The transcriber's note must include a drawing of any sign for which there is no equivalent symbol in the Code.

(1)

#13de7

(a base-12 numeral in which &dek; represents 10 and ⪙ represents 11. Here the transcriber has assigned d to &dek; and E to ⪙)

verbose semantics

Number 1 3 d e 7

c. Another common technique is to use an arbitrary set of signs which do not include Arabic digits. In this case, the transcriber must proceed as in b above.

(1)

#apd

(a base-3 numeral of three digits; here the transcriber has assigned A to @, P to %, and D to $)

verbose semantics

at-sign percent dollar-sign

d. The one-cell symbols which the transcriber uses to represent the digits of a non-decimal numeration system must be regarded as numeric symbols. As such, these numeric symbols are subject to the rules for transcribing numerals.

(1)

#t2e4

(a base-12 numeral; t and e are lower case in ink print)

verbose semantics

Number t 2 e 4

(2)

#3t.t8

(a base-12 numeral containing a decimal point between the second and third digits; t is lower case in ink print)

verbose semantics

Number 3 t point t 8

(3)

#fa9,b7c.0a

(a base-16 numeral containing a comma and a decimal point; F, A, B and C are capitalized in ink print)

verbose semantics

Number F A 9 comma B 7 C point 0 A

§14. Ordinal Endings: (See §55d.)

§15. Plural and Possessive Endings: (See §39.)

§16. Numerals in Diagrams: In diagrams which contain numeric labels, the numeric indicator must be used. The space to accommodate the numeric indicator may often be gained by a sufficient enlargement of the diagram.

§17. Numerals in Table Entries: In tables whose entries consist entirely of numerals, the numeric indicator must be omitted. However, in tables whose entries are a mixture of words, numerals, letters, or other mathematical signs, the numeric indicator must be used. This rule applies only to the body of a table and not to the headings. Determinants and matrices are not to be regarded as tables. The minus symbol is not numeric so that, if it occurs in a table, the numeric indicator must be used throughout the table.

§18. Roman Numerals:

a. Capitalized Roman numerals must be transcribed using the single capital sign before one letter and the double capital sign before more than one letter. For the use of the English-letter indicator with Roman numerals, see §28c.

(1)

;,i, ,,ii, ,,iii, ,,iv, ;,v_4

verbose semantics

Upper I comma UpperWord I I comma UpperWord I I I comma UpperWord I V comma Upper V period

(2)

,! lrs ;,i, ;,V, ;,x, ;,l, ;,c,
  ;,d, ;,m >e ! symbols we use 
  5write ,roman num]als4

verbose semantics

The letters Upper I comma Upper V comma Upper X comma Upper L comma Upper C comma Upper D comma Upper M are the symbols we use to write Roman numerals period

(3)

,,vii+,v .k ,,xii

verbose semantics

UpperWord V I I plus Upper V equals UpperWord X I I

(4)

(,i+,,ii)+,,iii
   .k ,i+(,,ii+,,iii)

verbose semantics

left-parenthesis Upper I plus UpperWord I I right-parenthesis plus UpperWord I I I equals Upper I plus left-parenthesis UpperWord I I plus UpperWord I I I right-parenthesis

(5)

,,ii'

(prime sign follows the Roman numeral)

verbose semantics

UpperWord I I prime

(6)

,m:

(bar over M)

verbose semantics

Upper M over-bar

(7)

,v .k #5, ,l .k #50_4

verbose semantics

Upper V equals 5 comma Upper L equals 50 period

(8)

,r1d *apt]s ;,i-;,v &
   ,,xi-,,xv_4

verbose semantics

Read chapters Upper I hyphen Upper V and UpperWord X I hyphen UpperWord X V period

(9)

#1_4
  (,i)
  (,,ii)

verbose semantics

StartLayout 1st Row 1st Column 1 point 2nd Column Blank 2nd Row 1st Column Blank 2nd Column left-parenthesis Upper I right-parenthesis 3rd Row 1st Column Blank 2nd Column left-parenthesis UpperWord I I right-parenthesis EndLayout

(10)

#1_4
  ;,i_4
  ,,ii_4

verbose semantics

StartLayout 1st Row 1st Column 1 point 2nd Column Blank 2nd Row 1st Column Blank 2nd Column Upper I period 3rd Row 1st Column Blank 2nd Column UpperWord I I period EndLayout

b. When a roman numeral consists of one or more lower-case letters it must be treated as though it were a "single letter" and, as such, the English-letter indicator must be used or not used in accordance with the rules governing the English-letter indicator (see §§26-28).

(1)

;i, ;ii, ;iii, ;iv, ;v_4

verbose semantics

i comma i i comma i i i comma i v comma v period

(2)

,see pages ;v & ;vi_4

verbose semantics

See pages v and v i period

(3)

@,pa, @,si & @,sii_4

verbose semantics

paragraph-mark a comma section-mark i and section-mark i i period

(4)

vi+iv .k x

verbose semantics

v i plus i v equals x

(5)

i .k #1, v .k #5, & x .k #10_4

verbose semantics

i equals 1 comma v equals 5 comma and x equals 10 period

(6)

,r1d pages ;i-;v & ;xi-;xv_4

verbose semantics

Read pages i hyphen v and xi hyphen xv period

(7)

#1_4
  (i)
  (ii)

verbose semantics

StartLayout 1st Row 1st Column 1 point 2nd Column Blank 2nd Row 1st Column Blank 2nd Column left-parenthesis i right-parenthesis 3rd Row 1st Column Blank 2nd Column left-parenthesis i i right-parenthesis EndLayout

(8)

#1_4
  ;i_4
  ;ii_4

verbose semantics

StartLayout 1st Row 1st Column 1 point 2nd Column Blank 2nd Row 1st Column Blank 2nd Column i period 3rd Row 1st Column Blank 2nd Column ii period EndLayout

c. When it is questionable that a letter combination is a Roman numeral, treat the combination as if it is not a Roman numeral.

(1)

,c,l

(this combination occurs in a context from which it cannot be ascertained whether CL is a Roman numeral)

verbose semantics

CL

(2)

mix

(this combination occurs in a context from which it cannot be ascertained whether mix is a Roman numeral)

verbose semantics

mix

d. For punctuation of Roman numerals, see §37, iii.

§19. Spacing with Numerals: Spaces within numerals must be left when it is necessary to partition a numeral into short regular segments, or to achieve alignment. (For examples see §11b and c.)