Percentages are one of the mathematical tools we come across most often in everyday life: from discounts in shops to statistical data on the news, from bank interest rates to measurement errors in the laboratory. In this chapter we learn to handle them rigorously. We start from the basic idea — a percentage is always a fraction of something — and from the fundamental rule of increases and reductions. We then discover that increases and reductions do not cancel each other out and that percentage changes multiply, they do not add up. On this idea we build three fundamental applications: discounts, VAT and the commercial mark-up; simple and compound interest, with the surprising difference in growth over the long term; and finally the percentage as a measure of change, that is the relative error we shall use in physics and in statistics.
Sections
- Basic percentages
- Discounts, VAT and commercial mark-up
- Simple interest and compound interest
- Percentage as change: relative error