Add. THE FOUR OPERATIONS 68. $988.058, $75.896, $75, $68.299, $86.43, $45.256. 69. $77.948, $89.23, $57.637, $88.009, $6.783, $.086, $55. 70. $235.06, $578.085, $735.88, $967.08201, $ 3.6872, $ 20.98, $66, $8.7963, $48.23415, $9996.6, $ 8763. NOTE. The pupil should turn to p. 54 and solve examples 141 to 145, carry ing out each quotient two or three decimal places. 7)2.000000 .285714 Our last remainder is 2, and the next dividend is 20, what we had at first. Hence, the quotient will repeat the figures 2, 8, 5, 7, 1, 4, and will not come out exact. It is, therefore, impossible to reduce to a decimal exactly. 7)2.000000 If we desire to show the figures which repeat, we carry out the division until the quotient begins to repeat, and place dots over the first and last figures of the repetend, as in III. The result is a circulating decimal; it is read: decimal, repetend, 2, 8, 5, 7, 1, 4, repetend. 103. What fractions cannot be reduced to decimals exactly? Ans. Those fractions which have prime factors other than 2 or 5 in their denominators. The factors of 10 are 2 and 5. Hence, if a fraction has any prime factor other than 2 or 5 in its denominator, the reduction will not be exact. 104. Can 105. If be reduced to a decimal exactly? Why? is reduced to a decimal exactly, how many decimal places will there be in the result? Ans. 8. = × × × × × 1 × 1 × ↓ = (.5)8. 131 Can be reduced to a decimal exactly? Why? 132. Reduce 1 to a decimal, writing the divisor under the remainder after the third decimal place of the quotient. 133. Reduce to a decimal, writing+' after the fourth decimal place of the quotient. 134. Reduce to a circulating decimal, writing dots over the first and last figures of the repetend. COMPLEX DECIMALS If a complex decimal is to be subjected to any operation, it is best first to reduce to a simple decimal. 135. Prepare 36.001, 7.13 for the operations. 36.00 36.0025; 7.1 = = 7.1375 When a complex decimal cannot be reduced to a simple decimal, it is generally sufficient to carry out to three or four decimal places and to substitute'+' for the common fraction. 136. Prepare 16.21, 48.325 for the operations. 16.216.233+; 48.325 = 48.328+ If absolute accuracy is required, the common fraction cannot be neglected. 137. Add exactly 16.21, 48.325. 16.2 = 16.23 48.32=48.325 64.56 Since is tenths and is hundredths, it is necessary to reduce to hundredths. In division, it is frequently possible to simplify by multiplying both dividend and divisor by some number. CIRCULATING DECIMALS If a circulating decimal is to be subjected to any operation, it is best first to reduce to a common fraction. To reduce a circulating decimal to a common fraction, for the numerator, write the repetend, and for the denominator as many 9's as there are figures in the repetend. 140. Reduce 15 and .207 to common fractions and illustrate the rule. |