ADDITION OF DECIMALS. 1. Q. What is the rule for adding Decimals? A. Place the given numbers so that the Decimal points may stand directly under each other, then add as in whole numbers. 2. Q. In the addition of Decimals what is the rule for pointing of? A. Point off so many places for decimals as are equal to the greatest number of Decimals in the given PRACTICAL QUESTIONS. 1st. Add together 4,123; 45,0065; 79,3; 37,0008; and ,000009. Ans. 165,430309. 2d. What is the amount of three hundred seventy-tive and nine tenths, seventy-four and twenty-five hundredths, eleven and eighteen millionths, and fifteen, and two hundred thirteen hundred thousandths? Ans. 476,152148. 3d. Required the amount of $340 thirty-nine hundredths; $291 nine hundredths; $136 nine hundred ninety-nine thousandths and $12 one tenth? Aus. $780.579. Or thus, $310 thirty-nine cents; $291 nine cents; $136 ninety-nine cents, nine mills, and $12 ten cts. Ans. $780 57 cts. 9 m. NOTE. This is to show the scholar that calculations in federal money are the same as in Decimals,and that dimes, cents and mills are decimal parts of a Dollar, which is sufficient proof that a knowledge of decimals is absolutely necessary. SUBTRACTION OF DECIMALS. 1. Q. What is the rule for subtracting Decimals? A. Place the given numbers the same as in Addition, and subtract as in whole numbers. 2. Q. What is the rule for pointing off decimals in Subtraction? A. The same as in Addition. 5th. Borrowed $109.25; paid $87.09; how much is due? $22.16 6th. From four hundred and eighty, take seventy-five and seventy-five millionths. Rem. 404.999925. MULTIPLICATION OF DECIMALS, 1. Q. How is Multiplication of Decimals performed? A. The same as Simple Multiplication. 2. Q. What do you observe with regard to pointing off Decimals in Multiplication? A. Point off as many figures from the product as there are decimal places in both the Factors; but if the product should not have so many, supply the defect by prefixing cyphers. Multiply 52,238 by 12,17 Multiply,3759 by,945 Multiply one hundred thirty-five sandths by nine and three tenths. By ,0605 41520 50824 ,5123920 Multiply three thousand seven hundred fifty-nine ten thousandths by nine hundred thousandths. Prod. 000033831. The following answers are not pointed, that the learner may exercise his own judgment. Mult. 5,236 by ,008 Prod. 041888 Prod. 674352 Prod. 30714646 When the multiplier is an unit or one with any number of ciphers, as 10, 100, &c. remove the separatrix so many places to the right hand as there are ciphers in the multiplier. Multiply ,54367 by 10 Multiply ,54367 by 1000 Multiply ,54367 by 10000 Prod. 5,4367 PRACTICAL QUESTIONS. 1st. What cost 10 gallons W. I. Rum at,851*cts. per gallon? Ans. $8,55 * In decimals signifies five-tenths, and must be written twenty-five hundredths seventy-five hundredths ,25 5 2 2d. What will 91 lb. beef steak come to at 6 cts. per lb. Ans. ,6175 613 cts. 3d. What cost 25 lb. sugar at 121 cts. 4th. What cost 30 lb. tea at $1,25. 5th. What cost 8 lb. tea at $13? 6th. What cost 10 gal. wine at $11 per gal.? Ans. $3,125 Ans. $37,50. Ans. $14 Ans.$12,5 7th. What cost 4 bu. corn at ,551 cts. per bushel? Ans. $2,4975-$2,493. 8th. What cost 15 cwt. iron at 5,50 per cwt? Ans. $82,50. 9th. What cost 1,225 ft. board at $9,5 per M.? Ans. $11,6375-$11,633. 10th. What cost 30,313 ft. boards at $8,25 per M.? Ans. $250,0821. 11th. What cost 516 ft. boards at 10 cts. per ft. ? Ans. $51,60 12th. What cost 75 ft. boards at 8 cis. per ft. ? Ans. $6. 13th. What cost 11 2 apples at 9 mills per apple? Ans. $1,008. 14th. What cost 37 oranges at half a cent each? Ans. $0.185 15th. What cost 50 marbles at 1 cts. each? DIVISION OF DECIMALS. Ans. $0,75 1. Q. How is Division of Decimals performed? A. The same as Simple Division. 2. Q. What is the rule for pointing in Division? A. Pointoff so many places as the decimal places in the Dividend exceed those in the Divisor. If the places of the Quotient be not so many as the rule requires, supply the defect by prefixing ciphers. 3. Q. When the decimal places in the Divisor and Dividend are equal, what will be the quotient ? A. An integer. 4. Q. Should the divisor have more Decimal places than the dividend what must be done' A. Annex so many ciphers to the dividend, as will make up the deficiency. 5. Q. Should there be a remainder at any time, how must it be treated? A. Ciphers may be annexed and the quotient carried to any degree of exactness.* 6. Q How far will it be necessary to carry the quotient? A. Four or five places of decimals will be enough, and generally, three will be sufficient. Every cipher that is annexed must be counted as a decimal place in the dividend. † (+) Signifies more or that after obtaining the quotient there is still a remainder. |