From the example of 1/3 that we have just seen (and many more that we could mention), we know now that some fractions have no exact decimal equivalents. For those cases, the best we can find for a decimal representation will be an approximation. We can make the decimal approximation as close as we like by using larger and larger numbers of digits, but in the end, no decimal number will show the exact value in every case. On the other hand, some fractions may actually have exact decimal equivalents, but the number of their required digits may be too large to practically display on a page, form, monitor, or calculator. In the final analysys, the decimal number system is a device that is for displaying numbers approximately and not exactly.