Hints for some typical problems

Calculations involving proportions or ratios
The 'unitary method' is a useful way of approaching calculations involving proportions or ratios, such as those required when making up solutions from stocks or as a subsidiary part of longer calculations.

• If given a value for a multiple, work out the corresponding value for a single item or 'unit'.
• Use this 'unitary value' to calculate the required new value.

Calculations involving series
Series can be of two main forms:

1. arithmetic, where the difference between two successive numbers in the series is a constant, e.g. 2, 4, 6, 8, 10, ... ;
2. geometric, where the ratio between two successive numbers in the series is a constant, e.g. 1, 10, 100, 1000, 10000, ....

Note that the logs of the numbers in a geometric series will form an arithmetic series (e.g. 0, 1, 2, 3, 4, ... in the above case). Thus, if a quantity y varies with a quantity x such that the rate of change in y is proportional to the value of y (i.e. it varies in an exponential manner), a semi-log plot of such data will form a straight line. This form of relationship is relevant for chemical kinetics and radioactive decay.

Statistical calculations
The need for long, complex calculations in statistics has largely been removed because of the widespread use of spreadsheets with statistical functions and specialized programs such as Minitab^®. It is, however, important to understand the principles behind what you are trying to do and interpret the program's output correctly, either using the 'help' function or a reference manual.