ADDITION OF DECIMALS. RULE. "1. PLACE the numbers, whether mixed or pure decimals, under each other, according to the value of their places." "2. FIND their sum as in whole numbers, and point off so many places for decimals as are equal to the greatest number of decimal places in any of the given numbers." EXAMPLES. 1. What is the amount of 73,612 guineas, 436 guineas, 3,27 guineas,,8632 of a guinea, and 100,19 guineas, when added together? OPERATION. 436, 3,27 ,8632 100,19 Ans. 613,9352 guineas. 2. 345,601 ,3724 63,1 572,813 7,5462 THE decimals are arranged from the separatix towards the right hand and the whole numbers from the same point towards the left hand. The greatest number of decimal places in any of the numbers is four, consequently, four figures in the product must be pointed off for decimals 3. REQUIRED the sum of 37,821+ 546,358,437,325 ? Answer, 629,896 4. WHAT is the sum of three hundred twenty nine and seven tenth; thirty seven and one hundred sixty two thousandths and sixteen hundredths when added together? Answer, 367,022. 5. ADD six hundred and five thousandths, and four thousand & three hundredths? Sum, 4600,035 NOTE. When the numerator has not so many places as the denominator has cyphers, prefix so many cyphers at the left hand as will make up the defect; so is written thus,005. &c. 100 SUBTRACTION OF DECIMALS. RULE. "PLACE the numbers according to their value; then subtract as in whole numbers, and point off the decimals as in addition." ALL the operations in Decimal Fractions are extremely easy; the only liability to error will be in placing the numbers and pointing off the decimals; and here care will always be security against mistakes. MULTIPLICATION OF DECIMALS. RULE. 1. WHETHER they be mixed numbers, or pure decimals, place the factors and multiply them as in whole numbers." "2. POINT off so many figures from the product as there are decimal places in both the factors; and if there be not so many decimal places in the product, supply the defect by prefixing cyphers." 1. THE places of decimal parts in the divisor and quotient counted together must be always equal to those in the dividend, therefore divide as in whole numbers, and, from the right hand of the quotient, point off so many places for decimals, as the decimal places in the dividend exceed those in the divisor. 2. If the places of the quotient be not so many as the rule requires, supply the defect by prefixing cyphers to the left hand. "3. Ir at any time there be a remainder, or the decimal places in the divisor be more than those in the dividend, cyphers may be annexed to the dividend, or to the remainder, and the quotient carried on to any degree of exactness." In division of decimals it is proper to add cyphers so long as there continues to be a remainder, this however is not practised nor is it necessary; four, or five decimals being sufficiently accurate for most calculations. REDUCTION OF DECIMALS. CASE 1. To reduce Vulgar Fractions to Decimals. ANNEX a cypher to the numerator and divide it by the denominator, annexing a cypher continually to the remainder. The quotient will be the decimal required. 3. REDUCE, and to decimals. Answers,,25.,5.,75. 4. REDUCE, and, to decimals. Ans.,1923+,025,00797+ CASE, 2. To reduce numbers of different denominations, as of money, weight and measure, to their decimal values. RULE. "1. WRITE the given numbers perpendicularly under each other for divi "dends, proceeding orderly from the least to the greatest. L |