Common ways percentages can mislead you

When dealing with percentages, there are some ways in which they can fool you. They can act in a way that simply does not seem correct, or does not match our intuition.

Percentages do not cancel out

If I increase something by say 20% then reduce it by 20% you might expect to get back to the number you started with. But you don't!.

For example, if I have 100 items and reduce that by 20% I get 80 items: Now if I increase 80 by 20% I get 96: So I end up with 96 items, not 100.

Why? Because in the first percentage I am taking 20% of 100 which is 20. In the second percentage I am taking 20% of 80 which is 16.

A common mistake in investing

This misunderstanding happens frequently in investing. If I own an investment and it goes down 25% in value, I now need it to go up in value by 33.3% to return to where I started. Say I start with the investment value of $1000: So my investment has dropped by $250 to $750. To get back to $1000, I need to know what percentage $250 is of $750, which is one third, or 33.3%.
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Other fractions, percents, ratios topics