Jubmitted to the public, not without a hope that will be found, in fome degree, useful to our country Schools. THE AUTHOR. Worcefter, May, 1802. + EXPLANATION of the CHARACTERS. The fign of addition ; a8, 4+4; which denotes that 4 is to be added to 4. The fign of fubtraction; as, 8-4; which denotes that 4 is to be taken from 8. The fign of multiplication; as, 7×81 which denotes that 7 is to be multiplied by 8. The fign of divifion; as, 82; which {denotes that & is to be divided by a The fign of equality; as, 4+3=7; The fign of proportion; thus, 3: 6 THE PUPILS's GUIDE, &c. ARITHMETIC is the art of reckoning by numbers, and is founded on the five following rules, viz. Numeration, Addition, Subtraction, Multiplication, and Divifion. By the right applica tion of these, all other rules of Arithmetic are wrought. NUMERATION. NUMER TUMERATION teaches to exprefs any number, composed of these ten characters; 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. The first nine of thefe, or rather all of them, are called figures or digits-o is called nought, or cypher; and when alone, is of no fignification; but when annexed to the right hand of other figures, it makes the number ten times as much as it was before; thus, 7, by annexing a cypher, (70) becomes feventy. When a number of figures are fet together, the first, at the right hand, represents its own 1 value; that in the fecond place, ten times its own value; that in the third place, a hundred times its own value, &c. according to the following table. In the foregoing table, I have divided the figures by commas into periods of three figures each. The firft period. (beginning at the right hand,) is a period of units; the fecond is a period of thousands; the third is a period of millions. The first figure at the right hand of the firft period is one; the two firft, taken together, are twenty one; and the whole period is three hundred and twenty one. The first figure of the fecond period is four thousand; the two first, taken together, are fifty four thousand; and the whole period is fix hundred and fifty four thousand. The first figure of the third period is feven millions; the two firft are eighty feven mil lions; and the whole period is nine hundred and eighty feven millions; which, joined to the other two periods, is nine hundred and eighty feven millions, fix hundred and fifty four thousand, three hundred and twenty one, 987,654,321. In like manner, you may enumerate figures which stand in a different order from thofe in the table. In feparating them into periods, you must begin at the right hand, and proceed towards the left; but in expreffing their value, you must begin at the left hand, and read towards the right. A TABLE to enumerate a greater number of figures. 3 2 1,9 8 7 6 5 4 3 2 1,9 7, You may proceed in the fame manner from billions to trillions, quatrillions, quintillions, fextillions, feptillions, octillions, nonillions, decillions, &c. Billions are millions of millions; Trillions are millions of millions of millions; Quatrillions are the 4th degree of millions; Quintillions are the 5th degree of millions; Sextillions are the 6th degree of millions, &c. APPLICATION. Write down in figures the following numbers. 1. Two hundred and four.* 2. Four thoufand, three hundred. 3. Eleven thousand and forty four. 4. One hundred and fifty feven thousand, one hundred and five. 5. Nine million, fix thousand, one hundred and fifty two. 6. Fourteen million and a half. Write down in words the following numbers. *Thofe places of the natural order, which are omitted in the question, must be supplied with exphers. |