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Discrete transforms play an important role in digital signal processing. In particular, due to its transform domain energy compaction properties, the discrete cosine transform (DCT) is pivotal in many image processing problems. This paper introduces a numerical approximation method for the DCT based on round-off techniques. The proposed method is a multiplierless technique with low arithmetic complexity. Emphasis was given to approximating the 8-point DCT. A fast algorithm for the introduced 8-point approximate transform was derived. An application in image compression was examined. In several scenarios, the utilization of the proposed method for image compression resulted in comparable or better performances, when compared to the usual DCT-based methodology.