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.
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%.
Other fractions, percents, ratios topics
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