Mathematical operations and error analysis

Because the accuracy of every measurement matters so much in analytical chemistry, and because every real measurement carries some intrinsic error, the numerical data collected in an experiment has to be treated mathematically before it can support a sound quantitative conclusion. This means an analytical chemist needs three related skills: knowing how to report quantitative data in a way that honestly shows the extent of its accuracy, knowing how to correctly carry out arithmetic operations (addition, subtraction, multiplication, division) on numbers that come from measurements of differing accuracy, and knowing how to properly express the resulting error in a calculated result. The rest of this section works through each of …