Nine tens and nine or ninety-nine is the largest number that can be expressed by two figures. If one be added to nine tens and nine, it makes ten tens, or one hundred. To express one hundred we use the first figure again; but in order to show that it has a new value, it is put in another place, which is called the hundreds' place. The hundreds' place is the third place counting from the right. One hundred is written, 100; two hundred is written, 200; three hundred is written, 300. The zeros on the right have no value; their only purpose is to occupy the two first places, so that the figures 1, 2, 3, &c. may stand in the third place. The figures in the second place, we observe, have the same value whether the first place be occupied by a zero or by a figure for example, in 20 and in 23 the 2 has precisely the same value; it is two tens or twenty in both. In the first there is nothing added to the twenty, and in the second three is added to it. : It is the same with figures in the third place. They have the same value, whether the two first places are occu pied by zeros or figures. In 400, 403, 420, and 435, the 4 has the same value in each, that is four hundred. The value of every figure, therefore, depends upon its place as counted from the right towards the left. A figure standing in the first place signifies so many units; the same figure standing in the second place significs so many tens; and the same figure standing in the third place signifies so many hundreds. For example, 333, the three on the right signifies three units, the three in the second place signifies three tens or thirty, and the 3 in the third place signifies three hundreds. The number is read three hundreds, three tens, and three, or three hundred and thirty-three. We have seen that all the numbers from ten to twenty, from twenty to thirty, &c. are expressed by adding units to the tens; in the same manner all the numbers from one hundred to two hundred, from two hundred to three hundred, &c. are expressed by adding tens and units to the hundreds.-For example, to express five hundred and eighty-two, we write five hundreds eight tens, and two units thus, 582. The largest number that can be expressed by three figures is 999, nine hundreds, nine tens, and nine units, or nine hundred and ninety-nine. If to this we add one unit more, we have a collection of ten hundreds, which is called one thousand. To express this, the 1 is used again; but to show that it expresses 1 thousand it is written one place farther to the left, that is, in the fourth place, thus 1000. Two thousand is written 2000, and so on, to nine thousand, which is written 9000. The intermediate numbers are expressed by adding hundreds, tens, and units to the thousands. It is easy to see that this manner of expressing numbers may be continued to any extent. Every time a figure is removed one place to the left its value is increased ten-fold, and since nothing limits the number of places which we may use, there can be no number conceived, however large, which cannot be expressed with these nine characters. We sometimes call the figures in the first place or right hand place, units of the first order; those in the second place, or the collection of tens, units of the second order ; those in the third place, or the collection of hundreds, units of the third order, &c. The following table exhibits the first nine places or orders, with their names, and contains a few examples to illustrate them. Hundreds ∞ Tens In looking over the above examples it will be observed, that the three first places on the right have distinct names, iz. units, tens, hundreds; and that the three next places are all called thousands, the first being called simply thousands ; the second, tens of thousands; the third, hundreds of thousands. In the same manner there are three places appropriated to millions, and distinguished in the same way, viz. millions, tens of millions, hundreds of millions. The same is true of all the other names, three places being appropriated to each name. From this circumstance it is usual to divide the figures into periods of three figures each. This division very much facilitates the reading and writing of large numbers. Indeed it enables us to read a number consisting of any number of figures, as easily as we can read three figures. This is illustrated in the following example. Units → Hundreds Units Hundreds → Tens Units Tens 3 8 5,6 7 9,2 5 8,6 7 3,4 6 2,9 2 7,6 4 8 We have only to make ourselves familiar with reading and writing the figures of one period, and we shall then be able to read or write as many periods as we please, if we know the names of the periods. It is to be observed that the unit of the first period is simply one; the unit of the second period is a collection of a thousand simple units; the unit of the third period is a collection of a thousand units of the second period, or a mil lion of simple units; and so on as we proceed towards the left, each period contains a thousand units of the period next preceding it. The figures of each period are to be read in precisely the same manner as the figures of the right hand period. At the end of each period, except the right hand period, the name of the period is to be pronounced. The right hand period is always understood to be units without mention being made of the name. In the above example, the right hand period is read, six hundred and forty-eight (units being understood.) The second period is read in the same manner, nine hundred and twentyseven, but here we must mention the name of the period at the end; we say, therefore, nine hundred and twenty-seven thousand. If we would put the two periods together, we begin on the left and say, nine hundred and twenty-seven thousand, six hundred and forty-eight. The third period is read four hundred and sixty-two, adding the name of the period, it becomes four hundred and sixty-two millions: and the three periods are read together, four hundred and sixty-two millions, nine hundred and twenty-seven thousand, six hundred and forty-eight. Beginning at the left hand of the above example, the seve ral periods are read separately as follows-three hundred and eignty-five; six hundred and seventy-nine; two hundred and fifty-eight; six hundred and seventy-three; four hundred and sixty-two; nine hundred and twenty-seven; six hundred and forty-eight. Giving each period its name and putting all together as one number, it becomes three hundred and eighty-five quintillions; six hundred and seventy-nine quadrillions; two hundred and fifty-eight trillions; six hundred and seventy-three billions; four hundred and sixty-two millions; nine hundred and twenty-seven thousand; six hundred and forty-eight. The names of the periods are derived from the Latin numerals, by giving them the termination illion and making some other alterations, so as to render the pronunciation easy. After quintillions come sextillions, septillions, octillions, nonillions, decillions, undecillions, duodecillions, &c. A number dictated or enunciated, is written by beginning at the left hand, and proceeding towards the right, care being taken to give each figure its proper place. If any place is omitted in the enunciation, the place must be supplied with a zero. If, for example, the number were three hundred and twenty-seven thousand, and fifty-three; we observe that the highest period mentioned is thousands, which is the second period, and that there are hundreds mentioned in this period, (that is, hundreds of thousands,) this period is therefore filled, and the number will consist of six places. We first write 3 for the three hundred thousand, then 2 im |