Classification is one of the most important techniques in data mining. Decision tree is the most important classification technique in machine learning and data mining. Decision tree classifiers are constructed using training dada sets. Training data sets contain numerical (or continuous) and categorical (or discrete) attributes. Measurement errors are common in any data collection process, particularly when training datasets contain numerical (or continuous) attributes. So, values of numerical attributes contain measurement errors in many training data sets. We extend certain (or traditional or classical) decision tree building algorithms to handle values of numerical attributes containing measurement errors. We have discovered that the accuracy of a certain (or classical or traditional) decision tree classifiers can be much improved if the measurement errors in the values of numerical attributes in the training data sets are properly handled (or controlled or modeled or corrected) appropriately. The present study proposes a new algorithm for decision tree classifier construction. This new algorithm is named as Accurate Decision Tree (ADT) classifier construction. ADT classifiers are more accurate than certain (or traditional or classical) decision tree classifiers. ADT proves to be more effective regarding classification accuracy when compared with Certain Decision Tree (CDT) classifiers. The performance of these two algorithms is compared experimentally through simulation.