Annuities, or Penfions in arrears, at Compound Intereft, 308 Annuities in Reversion, at Compound Intereft, --fhewing the prefent worth of £1 from 1 year to 40, 320 PIKE'S ARITHMETIC, ABRIDGED. A RITHMETIC is the Art or Science of computing by numbers, and is comprifed under five principal or fundamental Rules, viz. NOTATION or NUMERATION, ADDITION, SUBTRACTION, MULTIPLICATION and DIVISION. NUMERATION Teaches the different value of figures by their different places, and to read or write any fum or number by these ten characters, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9-0 is called a cypher, and all the reft are called figures or digits. 2. Befides the fimple value of figures, as above noted, they have, each, a local value, according to the following law; viz. In a combination of figures, reckoning from right to left, the figure, in the first place, reprefents its primitive fimple value; that in the fecond place, ten times its fimple value, and so on; the value of the figure, in each fucceeding place, being ten times the value of it, in that immediately preceding it. 3. The values of the places are estimated according to their order: The firft is denominated the place of units; the fecond, tens; the third, hundreds, and fo on, as in the Table. Thus in the number, 3467: 7, in the firft place, fignifies only feven; 6, in the fecond place, fignifies 6 tens, or fixty; 4, in the third place, four hundred; 3, in the fourth place, three thousand; and the whole, taken together, is read thus; three thousand four hundred and fixty feven. 4. A cypher, though it is of no fignification itself, yet, it poffeffes a place, and, when fet on the right hand of figures, in whole numbers, inereafes their value in the fame tenfold proportion; thus, 9 fignifies only nine ; but, if a cypher is placed on its right hand, thus, 90, it then becomes ninety. To enumerate any parcel of figures, obferve the following Rule. First, commit the words at the head of the Table, viz. units, tens, hundreds, &c. to memory; then, to the fimple value of each figure, join the name of its place, beginning at the left hand, and reading towards the right. More particularly-1. Place a dot under the right hand figure of the 2d, 4th, 6th, 8th, &c. half periods, and the figure over fuch dot will, univerfally, have the name of thoufands.-2. Place the figures 1, 2, 3, 4. &c. as indices, over the 2d, 3d, 4th, &c. period: Thefe indices, will then fhew the number of times the millions are involved the figure under 1, bearing the name of mil lions, that under 2, the name of billions (or millions of millions) that under 3, trillions (or millions of millions of millions.) EXAMPLE. EXAMPLE. Sextilli. Quintill. Quatrill. Trillions. Billions. Millions. Units. th. unth. un. th un th. un, th. un. th un. cxt.cxu. 913, 208;000, 341;620, 057;219, 356;809, 379;120, 406;129,763 NOTE, I. Billions is fubftituted for millions of millions Trillions, for millions of millions of millions: Quatrillions, for millions of millions of millions of millions. : Quintillions, Sextillions, Septillions, Otillions, Nonmillions, Decillions, Undecillions, Duodecillions, &c. anfwer to millions fo often involved as their indices refpectively denote. NOTE 2. The right hand figure of each half period has the place of units of that half period; the middle one, that of tens, and the left hand one, that of hundreds. The APPLICATION. Write down, in proper figures, the following numbers. Fifteen. Two hundred and feventy nine. Three thoufand, four hundred and three. Thirty feven thoufand, five hundred and fixty feven. Nine millions, feventy two thousand and two hundred. nine. Eight hundred millions, forty four thousand, and fifty five. Two thoufand, five hundred and forty three millions, four hundred and thirty one thoufand, feven hundred and two. Write down, in words at length, the following numbers. Notation by Roman Letters. -8 437 709040 3476194 7584397647 84094007 129 76506 4091875 690748591 49163189186 500098400700 I. One II. Two. III. Three. IV. Four. V. Five. VI. Six. VII. Seven. VIII. Eight. IX. Nine. X. Ten. XI. Eleven. XII. Twelve. XL. Forty. L. Fifty. LX. Sixty. CC. Two hundred. Il Five hund. thou. MDCCXCVIII. One thoufand feven hund. and ninety eight. A lefs literal number, placed after a greater, always augments the value of the greater; if put before, it diminishes it. Thus, VỊ is 6; IV is 4; XI is 11; IX is 9, &c. ADDITION Is the putting together of two or more numbers, or fums, to make them one total, or whole fum. SIMPLE ADDITION Is the adding of feveral integers or whole numbers together, which are all of one kind, or fort; as 7 pounds, 12 pounds, and 20 pounds being added together, their aggregate, or fum total, is 39 pounds. RULE. |