« ΠροηγούμενηΣυνέχεια »
NOTATION OF DECIMALS.
o Tens of millions,
In the above table, all the figures which stand at the left of the point, are integers (or whole numbers) and those at the right of it are decimals of one.
The first figure at the right of the point, taken alone, is called five tenths, i. e. if one is divided into ten equal parts, it is.five of those parts.
If the two next figures at the right of this. 5i be taken with it, they are called five hundred and twenty seven thousandths, &c.
NOTE 1. Ciphers annexed to decimal fractions do not alter their value, as 5.28 five tenths ; 50 is fifty hundredths ; 500 is five hundred thousandths : and each of them equal to one half of oné.
NOTE II. Ciphers prefixed' to decimals, diminish their value tenfold for each cipher so prefixed; as, ,5 is five tenths, ,05 are five hundredths, and ,005 are five thou-sandths, &c.
NOTE III. The point must always be prefixed to decimals, whether there are whole numbers at the left of them, or not ; otherwise they may be mistaken for whole numbers ;- thus 56. are fifty siž, but ,56 are fifty six kundredths of one ;, the first of these being a whole number; the second a decimal fraction.
A mixed number consists of whole and fractionali numbers, thus, 5g 2 are five; and two tenths ; 65, 03, are sixty fives, and three hundredths...
ADDITION OF DECIMALS. RULE. Place the numbers according to their value, i. e. units under units, tens under 'tens, also tenths under tenths, hundredths under hundredths, &c. and then proceed as in Simple Addition ; keeping the separating point in a perpendicular line.
EXAMPLES 4637, 532 736, 3
63, 5647 961, 003 9, 0006 3, 9036
006, 5362, 467 263, 6999
73, 0963 36, 4352 9038, 996 990, 9993 96, 4999 99, 4999 9906, 939 999, 4999 59, 4729 99, 9998 30009, 597
SUBTRACTION OF DECIMALS. Rule. Place the numbers as direeted in Addition, and then proceed as in Simple Subtraction.
EXAMPLES. 47, 036 ,9
47, 79, 96, 963 ,3648
,96 ,47 ,79 ,96
IN MULTIPLICATION OF DECIMALS. RULE. Proceed in all respects as in Simple Multiplication, till the product is found ; then point off as many decimal figures from the products, as there are in both factors taken together.
NOTE 1. If there are not so many figures in the produ. uct, as there are decimal figures in both factors taketti
together, prefix cifhers to them, till the number of places are supplied ; and then prefix a point at the left of them, and the whole will be decimal fractions.
Note II. Any number, either whole, fractiunal, or mixed, when multiplied by a fraction only, the product will be less than the multiplicand, in the same proportion as the multiplier is less than one.
IN DIVISION OF DECIMALS.
Rule. Proceed as in Simple Division, only observe, that the decimal places in the divisor and quotient, taken together, must be equal to those in the dividend ; and if there are not so many figures in the quotient and divisor, taken together, as there are decimal places in the dividend, prefix ciphers to the quotient, till the number is complete, then prefix a point, and it will be the true quotient.
If there are more decimal places in the divisor, than in the dividend, annex ciphers to the dividend, till the number of decimals are equal ; and then the quotient will be integers, or whole numbers : If there are remainders, and a more accurate quotient be required, annex as many ciphers to the remainder, as you would have decimal places in the quotient ; and divide this augmented remainder ; the quotient of which will be decimals.
NOVE. If any number, whole, fractional, or mixed, be divided by a decimal, the quotient will be greater than the dividend, in the same proportion as the divisor is less than
481875 867 375
Divide 9155,625, by 9,5. Divide 96 by ,573. 9,5)9155,625(96375 quot. ,573)96,000(167,556 quot. 855 and proof of 573
the example 605
Proof by multiplication. 3850
REDUCTION OF DECIMALS ; Or rather to reduce Vulgar to Decimal Fractions.
RULE. Sei down the numerator as a dividend, and divide it by the denominator, (after annexing a compe
tent number of ciphers to the numerator, or as many as you would have decimals.)
The quotient will be the decimal required, which, if, there be no remainder, is exact, but if any remains, it is deficient, which frequently happens ; the more decimal places are found, the nearer it approaches to a perfect decimal.
EXAMPLES. Let be reduced to a decimal. 28)7,00(,25 Ans. Proof by Multiplication. 56
7,00 Reduce to a decimal. 9)5,0000 Here is a remainder of 5, and
would be, if the division had been 95555 +5 continued, without end. "The 9 decimal being found to four plac
es, the remainder. is only of Proof. 5,0000 Todo, or five ninths of one ten
thousandths. Reduce to a decimal.
Ans. ,875. Here follow a number of Vulgar Fractions, with their decimals ; those which are not perfect have this sign of annexed.