Forty-two and is expressed by decimals. thus, 42; for if the numerator, which is 1, have a denominator 10 instead of 2, it will not express the true value, unless the numerator is increased in the same proportion as the denominator. But, as before observed, it is not necessary to use the denominator, as the figure next to units is always supposed to express tenth parts. Therefore we express it thus, 42,5 A Vulgar Fraction expressed thus, is supposed to mean that some particular number, or thing, as an apple or an orange, is divided into two parts, and that one of these parts is taken, but expressed thus, by decimals;,5 tells you that the apple is divided into 10 equal parts, and that 5 of those parts are meant, which, of course, must be equal to ;,05 means that the apple is divided into 100 parts, and that 5 of those parts are meant; ,005 supposes the apple to be divided into 1000 parts, and 5 of them are expressed by the fraction. Two and six tenths are expressed thus, 2,6. One hundred twenty-two, and three hundredths, thus, 122,03. Two hundred thirty-six, and four thousandths, thus, 236,004. 1. How many oranges and parts does the First number express, · 10,4 Any number is said to be a What is a mix-mixed number when it is ex ed number? pressed by a whole number, and a fraction of any value or kind. Express by figures the following numbers. 1. Three hundred twenty-nine, and seven tenths. 2. Thirty-seven, and one hundred and sixtytwo thousandths. 3. Six hundred, and five thousandths. 4. Four thousand, and three hundredths. 5. One thousand two hundred, and eightyfive hundredths. The operation of Addition, Subtraction, Multiplication and Division of Decimal Fractions, is precisely the same as in whole numbers, regard being paid to the manner of pointing off the Decimals. ADDITION OF DECIMALS. Rule. PLACE the numbers to be added, whether mixed or pure decimals, under each other according to the value of their places, and point off the decimals. 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? 73,612 436, 3,27 ,8632 100,19 Ans. 613,9352 guineas. How is the answer expressed by words? 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. WHETHER the given numbers be mixt numbers or pure decimals, multiply them as if they were all whole numbers, and when the product is found, point off so many decimal places as there are in both the multiplicand and multiplier, accounted together. 1. POINT off as many figures on the right hand of the 'quotient, as the decimal places in the dividend exceed those of the divisor. 2. If the places of the quotient be not so many as the rule requires, supply the defect by prefixing ciphers at the left hand. 3. If at any time there be a remainder, or the decimal places in the divisor be more than those in the dividend, ciphers may be annexed to the dividend or to the remainder, and the quotient carried on to any degree of exactness. Three or four places, however, are sufficient in common calculations. 2. Divide 2,735 by 51,2. 51,2)2,735(,0534+ 2,560 1750 1536 2140 92 In this example there are 5 decimals in the dividend, (counting the two ciphers which were added to the remainder of the dividend after the first division,) that the decimals in the divisor and quotient counted together may equal that number, a cipher is prefixed to the left hand of the quotient. 4. When there are not so many places of decimals in the dividend as the divisor, annex ciphers to the dividend to make them equal; then will the quotient be an unmixed whole number. |