College Algebra (10th Edition)

Rational numbers (fractions) can be converted to decimal numbers by dividing. For example $\frac{3}{4}$ can be converted to the decimal 0.75 by dividing 3.00 by 4. Some fractions will terminate when divided (such as the example $\frac{3}{4}$ above). However many fractions will not terminate when divided. For example when $\frac{3}{7}$ is divided out you get 0.428571428571....While $\frac{3}{7}$ doesn't terminate, you may notice it does have a repeating pattern of 428571. We know that any rational number will eventually repeat because there is a limited number of remainders you can get (for example with 7 the only possible remainders are 0, 1,2,3,4,5,6) so eventually the pattern must repeat. For this reason all rational numbers can be converted to decimal numbers that either terminate (stop) or repeat.