10. 27.48 by 6.73. 20. $450.00 by .0425. DIVISION OF DECIMAL FRACTIONS. 156. Any decimal number, whether integral or fractional, is divided by 10, 100, 1000, etc., by moving the decimal point to the left as many places as there are ciphers in the divisor. (Art. 150.) 157. Thus: 5976.÷10-597.6; 5976.÷100-59.76, etc. A dividend and divisor may both be either multiplied or divided by the same number without changing the quotient. (Art. 134, Principle X.) Thus 12÷4-3; multiplying both dividend and divisor by 4, 48÷16= 3; or, by dividing both terms by 4, 3÷1=3. This general principle is used in the analysis of the following examples : 158. 1. Divide 159.63 by .3. PROCESS. ANALYSIS. Multiply both dividend and divisor by 3)1596.3 10 by removing the decimal point. This changes the divisor .3, to the integer, 3, without changing the quo532.1 tient sought. Divide as in integers: 3 is contained in 15 hundreds 5 hundreds times; 3 is contained in 9 tens 3 tens times; 3 is contained in 6 units 2 units times; 3 is contained in 3 tenths .1 tenth times; that is, in general, when the quotient is an integer, each quotient figure is of the same order as the right hand figure of the partial dividend divided by it. Therefore, since the division of the unit figure of the dividend produces the unit figure of the divisor, when the divisor is an integer, place the decimal point in the quotient as soon as the decimal point in the dividend is reached. When the divisor is an integer, the number of decimal orders in the quotient is always equal to the number of such orders in the dividend. 1894 1792 1024 1024 ANALYSIS. Multiply both dividend and divisor by 100 by removing the decimal point, in order to change the divisor to an integer. Divide as in integers, placing the decimal point in the quotient when the decimal point in the dividend has been reached. 19. Divide 28.4967 by 5.84 to four decimal orders. 159. In each of the examples analyzed, the divisor has been changed to an integer unless it was already an integer. This has been done in order to make the process clear to the pupil. But it is not necessary in practice. Division is the converse of multiplication, (Art. 131.) the dividend being the product of the divisor and quotient. In Multiplication, the number of decimal orders in the product is always equal to the number of decimal orders in both factors; (Art. 153. ) and in Division, the number of decimal orders in the dividend is always equal to the number of decimal orders in both divisor and quotient, which are the two factors of the dividend. Therefore, to divide decimal fractions: Divide as in integers. the quotient as the Make as many decimal orders in number of decimal orders in the dividend exceed the number of decimal orders in the divisor. If necessary, prefix ciphers to the digits of the quotient. EXAMPLES. The teacher can determine to what extent such examples are needed. PROCESS. 4).0168 ANALYSIS. Divide each term by 1000 by erasing the three ciphers from the divisor, and removing the decimal point of the dividend three places to the left. (See Art. 150.) .0042 Divide: 16. The local value of any digit is determined by its position relative to the decimal point. 164. The Addition, Subtraction, Multiplication and Division of Decimal Fractions are governed by the same laws as are the corresponding operations of decimal integers, |