TABLE

FOR COMBINING THE DIFFERENT ORDERS OF UNITS INTO NUMBERS, FROM ELEVEN TO ONE HUNDRED, INCLUSIVELY.

A Table combining units indifferently to the sixth order.

Nine millions, four hundred and twenty-one, thousand, five hundred and forty-one.

five Seven millions, three hundred and eighty thou

one one

nine nine nine nine nine nine nine

sand, six hundred and five.

One million,seventy-three thousand, two hundred and ten.

Eight millions, one hundred and nine thousand, two hundred and ten. Eight hundred and seven thousand, and sixty. One million, one hundred and eleven thousand, one hundred and eleven.

Nine millions, nine hundred and ninety-nine thousand, nine hundred and ninety-nine.

NOTE. To read this Table, begin at the left, and read towards the right. The numbers, three, five, six, nine, eight, seven, and two, forming the first line, show the quantity

of units, and the head

ing at the top of each column, shows the order of units, which combined, make the number, (three millions, &c.,) in the left hand column, headed, numbers formed by their combination. A blank place occurring in any line of numbers, across the columns, shows that the order of units, mentioned at the top of the column, in which it occurs, must be left out of the number, which they form when combined. The preceding Table for combining the different orders of units into numbers, from eleven to one hundred, inclusively, is read in the same manner, e. g., the first two columns contain the number and order of units, (marked at the top,) and the third column, shows the number they form when combined. The learner should study this Table attentively, until he is able to tell, without difficulty, the number which any given quantity of units of the different orders, will form.

The Teacher may exercise the pupil by putting, at pleasure, such questions as the following:

1. What number can you form by three units of the eighth order; five units of the seventh order; four units of the sixth order; seven units of the fifth order; nine units of the fourth order; one unit of the third order; eight units of the second order, and two units of the first order?

2. What number can you form from seven units of the tenth order; eight units of the seventh order; nine units of the fifth order, and five units of the second order?

3. Combine four units of the twelfth order; four units of the ninth order; four units of the sixth order, and four units of the third order, into one number.

4. What is the combined value of seven units of the twentieth order; eight units of the fifteenth order; four units of the eleventh order; five units of the eighth order, and nine units of the fourth order?

If the learner is well acquainted with the table for analyzing numbers, he will answer these questions with ease.

Without continuing this subject further, we may see, without difficulty, that if we unite in the same way one unit of the third order, and one unit of the first order, we shall have one hundred and one; and if we combine ONE unit of the third order with Two units of the first order, we shall have one hundred and two, &c.; also, that ONE of the third order of units, (one hundred,) ONE of the second order of units, (ten,) and ONE of the first order of units, (one,) combined into one number, make one hundred and eleven, and in the same way we may compose all the intermediate numbers between a unit of the third order, (one hundred,) and a unit of the fourth order, (one thousand ;) thus, nine units of the third

order, (nine hundred,) nine units of the second order, (ninety, and nine units of the first order, (nine,) make nine hundred and ninety-nine, to which, if a unit of the first order, (one,) be added, we shall have one thousand, and so of all the other Periods.

Hence we conclude, that to compose numbers we must, First, designate the orders of units by particular names; Second, increase each order of units from one to nine, inclusively; and,

Third, unite the different orders of units, beginning with the highest, and retain the name of each as far as practicable; hence, we have the following

RULE for analyzing numbers.

First, inspect the given number from the right to the left, placing commas (,) on the right of the words which stand for the names of periods.

Second, supply the name of each period where it has been omitted; and,

Third, begin at the left, and repeat the name of each order of units, as they occur, according to the place they occupy in each period.

EXAMPLES.

1. Analyze four millions two hundred and fifteen thousand six hundred and twenty-one.

First, mark the periods, (with commas,) thus: four millions, two hundred and fifteen thousand, six hundred and twenty-one. Second, supply the name of each period where it has been omitted, thus: beginning at the left, and reading towards the right, and we have, first, four millions, (i. e., four units of millions ;) second, two hundred thousand; third, ten thou sand; fourth, five thousand: (since fifteen thousand equals ten thousand and five thousand ;) fifth, six hundred; sixth, twenty; and, lastly, one; hence, we have, first, FOUR units of the seventh order; second, Two units of the sixth order third, ONE unit of the fifth order; fourth, FIVE units of the fourth order; fifth, six units of the third order; sixth, Two units of the second order; and, seventh, ONE unit of the first order, which give the analysis required.

;

EXAMPLE II.

Analyze fifty-six billions, twenty-five millions, two hundred thousand and eighty-nine.

Ans. FIVE units of the eleventh order; six units of the tenth order; NONE of the ninth order; Two units of the eighth order; FIVE units of the seventh order; Two units of the sixth order; NONE of the fifth order; NONE of the fourth order; NONE of the third order; EIGHT units of the second order; and, NINE units of the first order.

NOTE. In this number (Example II.,) the places for units of the ninth, fifth, fourth, and third orders, are vacant, i. e., they are not expressed in the number; the rest are given, i. e., they are mentioned in the given number.

EXAMPLE III.

Analyze nine hundred and eighty-seven millions, six hundred and fifty-four thousand, three hundred and twenty-one.

EXAMPLE IV.

Analyze seven quadrillions, ninety-six millions and eightynine.

Ans. SEVEN units of the sixteenth order; NONE of the fifteenth order; NONE of the fourteenth order; NONE of the thirteenth order; NONE of the twelfth order; NONE of the eleventh order; NONE of the tenth order; NONE of the ninth order; NINE units of the eighth order; six units of the seventh order; NONE of the sixth order; NONE of the fifth order; NONE of the fourth order; NONE of the third order; EIGHT units of the second order; and, NINE units of the first order.

EXAMPLE V.

Analyze four hundred and sixty-seven thousand, three hundred and five.

EXAMPLE VI.

Analyze fifty-seven thousand, three hundred and eightyfour.

EXAMPLE VII.

Analyze four millions, seven hundred and ninety-six thousand, six hundred and eighty-seven.