A reliable scientific computation approach, substantially different from the known ones, based on Residue Number System (RNS) floating-point arithmetic is described. In the approach, the real number is represented by an expression which consists of two parts, the approximate part and the interval error part. The approximate part, represented by an RNS floating-point number, shows an approximate value for the real number. The interval error value, represented by two RNS floating-point numbers, shows the left and the right limit of an interval containing the error. In parallel to the result of operation, the rounding error induced by that operation is determined and then summed up in each operation. When a series of operations is completed, the range of existence for the result can be determined from the result of the computation and the sum of interval errors. For the illustration of the proposed method, some examples are also given, which are said to be difficult to find exact solution in the usual floating-point calculation.