A method of calculating real roots by a simple division process when an integral approximation is known is described. It is very powerful and economical in labour as well as being of extreme simplicity It surpasses Horner’s method in these respects and in many applications it is preferable to the Newton-Raphson method and others. A root is expressed directly in any scale of notation or, alternatively, as a continued fraction, and the processes involved would appear to be suitable for use in an automatic computer.