APPENDIX. I. TO ADD RECURRING DECIMALS. Rule 1. Convert the decimals into vulgar fractions, and add. Rule 2. Write down the decimals at length, under one another as in common addition, to three or four places more than are necessary to obtain two vertical columns alike; add as in common addition; the period will readily be seen in the result. EXAMPLE. Add together 1.0357, .5684, .345038. 1.03573573573573573 .56845684568456845 .34503834503834503 1.94923092645864921 Ans. 1.9492309264586. II. TO SUBTRACT RECURRING DECIMALS. Rule 1. Convert the decimals into vulgar fractions, and add. Rule 2. Write down the decimals, as in common subtraction, to four or five more places than are necessary to obtain two vertical columns alike; subtract as in common subtraction; the period will readily be seen in the result. Subtract .653 from 1.54302. EXAMPLE. 1.54302543025430254302 .65365365365365365365 .88937177660064888937 Ans. .889371776600648. III. TO MULTIPLY RECURRING DECIMALS. Rule 1. If the exact result is required, convert the decimals into vulgar fractions, and multiply; then re-convert the product into a decimal. Rule 2. If only an approximate answer be required, multiply by the abbreviated form for multiplication of decimals. Rule 1. Convert the decimals into vulgar fractions, and divide. Rule 2. If the divisor be not a recurring decimal, perform the division in the ordinary manner. Rule 3. If an approximate answer be required, divide by the abbreviated method for division of decimals. V. TO DETERMINE THE TOTAL NUMBER OF FIGURES WHICH THERE WILL BE IN ANY QUOTIENT. Rule. If the significant figures of the divisor represent a number not greater than the first equal number of significant figures in the dividend, the number of figures in the quotient will be equal to the difference between the numbers in the dividend and divisor, increased by 1. But if the figures of the divisor represent a larger number than the first equal number of figures in the dividend, the number of figures in the quotient will be equal to this difference. Thus in dividing 624309 by 8275, since 8275 denote a larger number than 6243, therefore there will be two figures in the quotient. Hence in division of decimals, knowing the whole number of figures in the quotient, and the number of decimals, we can easily find the number of integers or ciphers immediately after the decimal point. Thus in dividing 356.5043 by 7.253, since 7253 denote a larger number than 3565 therefore there will be 3 figures in the quotient, and since one must be a decimal, therefore 2 will be integers. Again in dividing .3565043 by 7.253, there will be 3 figures in the quotient, but there should be 4 decimals, therefore there must be one cipher after the decimal point. To find the sum of two numbers from the above Table. Look for one of them in the top line, and for the other in the left hand column the sum will be found in the square, which is underneath the one and in the same line with the other. To find the difference of two numbers from the above Table. Look in the left hand column for the less, and in the same line with this for the greater; the difference will be found at the head of the column in which the greater is. བམ། 21 24 27 30 33 36 4 8 12 16 20 24 5 28 32 36 40 44 48 10 15 20 25 30 35 40 45 50 55 60 6 12 18 24 30 36 42 48 54 60 66 72 7 14 21 28 35 42 49 56 40 48 63 70 77 84 8 16 24 32 11 22 33 44 55 66 77 88 99 110 121 132 To find the product of two numbers from the above Table. Look in the top line for one of them, and in the left hand column for the other; the product will be found in the square underneath the former, and in the same line with the latter. To find the quotient of a number not greater than 144 divided by a number not greater than 12 from the above Table. Look in the left hand column for the divisor, and in the same line with it for the dividend or the number next less than the dividend, the integral quotient will be found at the head of the column in which this number is found. I. TROY WEIGHT. penny weights ounces 480 = dwt. Oz. 5760 240 = 12 =1 Troy Weight is used for weighing gold, silver, jewels, liquor, &c. and in philosophical experiments. 24 = 8 = 1 288 = 96 = 12 = 1 Apothecaries' Weight is used for prescriptions. The grain, ounce. and pound are the same as in Troy Weight. VII. AVOIRDUPOIS WEIGHT. and precious stones. dr. Oz. lb. qr. cwt. Avoirdupois Weight is used for weighing all articles, except gold, silver. |