Excerpt from Arithmetic for High Schools and Collegiate Institutes Approximation is a part of arithmetic which has until lately been adequately discussed in only the higher classes of text-books, being, one might be led to conclude from their neglect of it, an unknown subject to the writers of the average school-book. But the great practical import ance of the subject is at length compelling its fuller recognition in school work, and it will receive more and more attention in proportion as arithmetical instruction ceases to be impractical and as teach ers become better acquainted with the requirements of the count ing-house, the workshop and the laboratory. In Chapter III, two methods of approximation are described; the first, Approximation by Continued Fractions; the second, Approximation by Abridgment of Decimal Computations. The former of these takes precedence in historical order and also on account of its theoretical simplicity and of the wide range of subjects to which it is applicable, - from the purely speculative questions of Farey'e series and the partitions of num ersto the laboratory problem of determining the formula of an organic com pound from its percentage composition - but the latter method is superior in facility of adaptation to all ordinary computations. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.