English Numerical Expressions

In English numerical expressions are divided into strings of three. For example, the number 357 contains a units’ place, a tens’ place, and a hundreds’ place. This first string may be called the

hundreds’ level. This basic ordering of places is repeated in the next higher level or string of three digits, which may be called the thousands’ level. This means that at the thousands’ level there are units, tens, and hundreds (of thousands). Moreover, the same pattern holds true for the next higher level, that is, the millions’ level. Once again, there may be units, tens, and hundreds (of millions). This system may be expanded to subsequently ever higher levels, practically ad infinitum. These facts are illustrated by the table in (3).

(3) Level of Hundreds Level of thousands Level of millions

Units 0-9 of one thousand 0-9 thousands 0-9 millions

Tens 10-99 of one thousand 10-99 thousands 10-99 millions

Hundreds 100 -999 of one thousand 100-999 thousands 100-999 millions

This system may be illustrated, for example, by the number 716, 429, 357. The strings of three digits are conventionally marked by commas in arithmetical notation. At the hundreds’ level we see 357; at the thousands’ level, 429, and at the millions’ level, 716. In the string of three digits at each of these levels there is a units’ place, a tens’ place, and a hundreds’ place.

When these numbers are given numeral expression, each of the levels contains the conjunction “and.” Thus, the number in our example is pronounced (without the emphasis suggested by the italics, which are provided for purely lexical demonstration) “seven hundred and sixteen million, four hundred and twenty nine thousand, three hundred and fifty-seven.”

Furthermore, something else is immediately noticeable from this numeral expression. Not only is “and” repeated at each level or in each string of three digits, but “hundred” is also repeated immediately preceding each “and.” This means that each string of string of digits is divided into two parts: the hundreds’ place on the left and a combination of the tens’ place and the units’

place on the right. The conjunction “and” stands in the middle of the division. This arrangement always occurs in English complex numbers, and it suggests a binary phrasal structure of two

constituents combined by co-ordination at each level or in each string of three digits. These observations are summarized in the generalizations given in (4).

(4) a. English numerals are arranged in strings of three digits, consisting of a units’ place, a tens’ place, and a hundreds’ place at each successively higher level of strings, beginning with the level of hundreds and proceeding to the level of thousands, the level of millions, and so on, virtually without limitation.

b. At each of the levels the morpheme “and” occurs following the morpheme “hundred.”

The effect of this is to bifurcate the string of three digits and suggest a phrasal structure with the hundreds’ place in the X position and a combination of the tens’ place and the units’ place in the Y position. Moreover, this suggested binary structure appears to be co-ordinated by “and.” Its function is additive.

Not all numbers, of course, contain all the possible places and strings. If (4) is true, what about a number such as 6,022? This number is pronounced “six thousand and twenty-two.” In this numeral expression “and” occurs after the word “thousand,” not the word “hundred.” There is a simple explanation for this. The morpheme “and” occurs after the hundreds’ place, but the hundreds’ place is occupied by “zero,” which is never spoken in English numeral expressions (except as 0 itself). The same might be said of the number 6,002, pronounced “six thousand and two.” Here again, “and” occurs after the hundreds’ place, and after the tens’ place as well, but both these places are phonetically null, though they are still present in LF. Therefore, such examples as these do not invalidate the generalizations in (4). In fact, the higher the number containing “and” but not “hundred” is, the more awkward and possibly ill-formed its expression sounds. For example, 76,000,003 is pronounced “seventy-six million and three,” but such an expression sounds somewhat strange.

Just as some numbers do not contain the morpheme “hundred” in their expression, other numbers do not contain the morpheme “and” in their expression. These numbers can be divided into two classes. The first of these classes contains the numbers 0-100, and the second of these

classes contains numbers over 100 that are composed of multiples of 1-100 combined with

various decimal multipliers, beginning with 100 and continuing with 1,000; 1,000,000; and so on.

The first class, numbers from 0-100, needs no illustration beyond random selection, say 4, 19, 42, 75, and so on. The second class, however, needs further explanation and illustration. For a number over 100 not to have “and” in its expression it must contain “zero” in both the tens’ place and the units’ place in the first string or at the hundreds’ level. An example would be 2,900 pronounced either “two thousand, nine hundred” or “twenty-nine hundred.” Hurford (2003, pp.

42-43) would prefer the first expression, because of what he calls the “packing strategy,” the idea that well-formed numerical expressions should contain the highest decimal multiplier, in this case 1000. He does admit, however, that an expression such as “twenty-nine hundred” also appears to be acceptable, though he cannot explain why. The important thing to note here is that the number ends with 0 in both the tens’ place and the units’ place at all levels The numeral could be any number from 1-100, and the multiplier could be any decimal beginning at 100.

Further examples would be 53,500 (“fifty-three thousand, five hundred”) and 49,000,000 (“forty-nine million”).

The first class of numerals that does not contain “and” is especially interesting.

Conventionally, the numbers 0-9 are considered to be simple numbers whose function it is to combine with other numbers, either through addition or multiplication, to form complex numbers (Hurford, 1975; Greenberg, 1978; and many others since). In other words, a complex number is either a sum or a product of two other numbers, one of which is usually a simple number and one of which is usually a decimal multiplier. Thus the number 37 is composed of multiplying the simple number 3 by the multiplier 10, attaining the product 30, and then adding the simple number 7, attaining the final sum 37. Nevertheless, in the light of this discussion there seems to be some justification for considering the numbers 0-99 as a distinct category of numbers in numerical expressions, mainly because they never contain “and.” These numerals are not separate lexical items, but within numerical expressions they behave as if they were lexical because they frequently occur both before multipliers and after “and” at the end of numbers Examples would be “twenty-three million,” “sixty-four thousand,” and “five hundred and twenty-four.”.

Thus we are led to another generalization, stated in (5).

(5) Within numerical expressions the numbers 1-99 often may be treated as separate lexical items. They often appear before higher multipliers beginning with 100, combining with them in phrasal structures. Their function here is multiplicative. The numbers 1-99 also appear after “and” at the ends of complex numbers. Their function in this case is additive.

Combining this generalization with the generalizations stated in (4) yields all the information needed to proceed with an interpretation of English numerical expressions within the framework of X-bar theory. To summarize: 1) English numerals are arranged in strings of three digits with a units’ place, a tens’ place, and a hundreds’ place; 2) the morpheme “and” appears after the hundreds’ place, suggesting an additive phrasal structure with two constituents joined by co-ordination; 3) numbers from 1-99 often appear before decimal multipliers and at the ends of complex numbers and can be treated as single lexical items in a multiplicative phrasal structure.

At the core of the English system of numerical expression is the frequent appearance of “and”

and its location after the hundreds’ place in strings of three digits at all levels.