Engineers Speak with Numbers

Numbers are expressed using figures (numerals). The first nonzero numeral at the left of a number (which contributes the largest amount to the number) is called the most-significant digit. The first nonzero numeral at the right of a number (which contributes the least amount) is the least-significant digit. All nonzero digits beyond the number of significant digits at the right of a number are removed in one of two ways: truncation or round off. Error propagates because of model-based derived quantities. A method or a result may become unstable due to the propagated error if the errors are magnified continuously during multiple derivations or iterative processes. Confidence levels can be defined through a good understanding of the nature (probabilistic distributions) of the errors. Designing a hypothesis testing starts with the choice of the level of significance since it directly affects whether to accept or reject a null hypothesis.