The author says that every real number x can be represented as x = m * 2^p where m is an integer(mantissa) and p is an integer (point position) Well this is

The author says that every real number x can be represented as x = m * 2^p where m is an integer(mantissa) and p is an integer (point position) Well this is clearly wrong, take x = 1/3 for example 1/3 = m * 2^p m = 1 / (3 * 2^p), where m is an integer, doesn't hold true for any integer p. If the author had read first 2 pages of https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.h... they could have avoided the embarrassment.