To change a pure circulate to a common fraction.
Rule.—Omit the (.) and write the figures of the repetend for the numerator, and as many 9’s for the denominator as there are places in the repetend.
Examples: Change the pure circulates .3̊, .2̊7̊, .1̊42857̊, to common fractions.
.3̊, (39 = 13) Ans. 1⁄3.
.2̊7̊, (2799 = 311) Ans. 3⁄11.
.1̊42857̊, (142857999999 = 17) Ans. 1⁄7.
To change a mixed circulate to a common fraction.
Rule.—From the whole decimal subtract the finite part, and make the remainder the numerator. For the denominator, write as many 9’s as there are figures in the repetend, and annex as many 0’s as there are finite places.
Example: Change the mixed circulates .16̊ and .416̊ to common fractions.
16 - 1 = 15, 1590 = 16. Ans. 1⁄6.