# Is negative percentage valid as per mathematics?

Can we have something like -2.5%? or (2.5)%

by (440 points)

In a word: yes. Negative percentages do have a real meaning. Percentages are simply ratios; in mathematics there's nothing wrong with having a ratio such as -1/2, just like there is nothing wrong with having a percentage of -50%.

A percentage just measures one variable with respect to another. Negative percentages typically occur when a certain variable changes with respect to another; in these cases, an increase will result in a positive percentage and a decrease will result in a negative percentage.

For instance, imagine that a business pulls in \$100 in profit one month and \$80 in profit the next month. That is, the business lost \$20 in profits over the second month. The *change* in monthly profits for this period is -20%. Similarly, if the same business makes \$120 instead of \$80 for the second month, then the business made \$20 in profits over the second month and the *change* in monthly profits is +20%.

Note the asterisks around the word "change." If the second month only provided \$80 profit, this is 80% of the first month, but the CHANGE in profit is -20%. The negative sign indicates that profits dropped 20%, from 100% to 80%. Note that all of these conventions signify the same thing mathematically.

by (16.5m points)

well it all depends

you can say you had 2.5% loss last year instead of using the word "negative"

by

Yes.

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