Chaotic systems are broadly adopted to generate pseudo-random numbers used in encryption schemes. However, when implemented on a finite precision computer, chaotic systems end up in dynamical degradation of chaotic properties. Many works have been proposed to address this issue. Nevertheless, little attention has been paid to exploit the finite precision as a source of randomness rather a feature that should be mitigated. This paper proposes a novel plain-image encryption using finite-precision error. The error is obtained by means of the implementation of a chaotic system using two natural different interval extensions. The generated sequence has passed all NIST test, which means it has sufficient randomness to be used in encryption. Several benchmark images have been effectively encrypted using the proposed approach.