EXERCISES. 2. Reduce .6 to a vulgar fraction. 3. Reduce .75 to a vulgar fraction. 4. Reduce .25 to a vulgar fraction. 5. Reduce .125 to a vulgar fraction. 7. Reduce .8125 to a vulgar fraction. CASE VII. When the decimal is a pure repetend. RULE. Under the given repetend place as many nines as there are figures in the repetend, for the denominator; then reduce the fraction to its lowest terms. EXERCISES. 2. Reduce .3 to a vulgar fraction. 9. Reduce .615384 to a vulgar fraction. CASE VIII. When the decimal is a mixed repetend. RULE. Subtract the finite part from the whole decimal, for the numerator, under which place as many nines as there are places in the repetend, and as many ciphers, on the right of these, as there are finite places in the decimal, for the denominator; then reduce the fraction to its lowest terms*. This and the former case will be better understood, after perusing the observations at page 102. G EXERCISES. 2. Reduce .06 to a vulgar fraction. 4. Reduce .07954 to a vulgar fraction. 5. Reduce to a vulgar fraction. 6. Reduce .213 to a vulgar fraction. 7. Reduce .2083 to a vulgar fraction. 8. Reduce .7621951 to a vulgar fraction. CASE IX. To make repetends similar and conterminous*. RULE. Extend the finite part of each, as far as the longest, and then extend all the circulates to as many places beyond that, as is expressed by the least common multiple of the number of places in each circulate. EXAMPLE. Make 14.3, 6.57, .123, and 321, similar and conterminous. 14.333333 6.575757 .123123 .321321 As the repetends, in this example, all begin at the same distance from the decimal point, it is only necessary to extend each of them to six places, the least multiple of 1, 2, and 3, the number of figures they contain. That is, begin and end at the same distance from the decimal point. EXERCISES. 2. Make .416, .63, and .396, similar and conterminous. 3. Make .23148, .90, and .10416, similar and conterminous. 4. Make .27, .09756, and .6, similar and conterminous. 5. Make .952743902, 38109756, and 5681, similar and con terminous. ADDITION OF DECIMALS. RULE. Arrange the decimal places under each other, according to their value, so that the decimal points may be directly under each other; then add the figures that stand in the same column, as in integers, and place the decimal point, in the sum, directly under the other points. EXAMPLE. Add together 65.24+1.397+563+.0046+1.525+29.076 +.25. 65,24 1.397 563. .0046 1.525 29.076 .25 660.4926 Sum. EXERCISES. 2. Add together 2.175 + 21.75+.0625+ 810+51.5+ 400.125+.00576. 3. Add together 376.25+86.125+637.4725+6.5+358.865 +41.02. 4. Add together 3.5+47.25 +927.01+2.0073+1.5. 5. Add together .01825+ 17.5+ .00375+ 199.25 +144+ 14310.0125. CASE II. When single repetends are given. RULE. 1. Extend the repeating figures one place beyond the farthest extended finite places, then add as before; only, in adding the right hand column, carry 1, for every 9 that it contains, to the next column. 2. The repeating figures may be converted into vulgar fractions, by Case VII, and then added, as directed in Addition of Vulgar Fractions*. EXAMPLE. Add together .83+7.416+6.25 +4.38+8.6. .833 7.416 6.25 4.388 8.666 27.545 Sum. *This mode of proceeding is more laborious than by the first part of the rule. |