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What is the value of the change in the percentage decrease? Given multiple values of percentage decrease, do we need consider the sign (i.e. '-') or just the numerical value is considered when comparing?

For example, -2%,-3% and -4% are the given percentage decrease from certain number, which one would be maximum decrease?

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    I think this is more of a semantics question than a math problem. I expect that most people would interpret "maximal decrease" to refer to the decrease which is largest in absolute value....hence $-4%$ in your example. Not sure I understand your first question. – lulu Aug 23 '18 at 14:19

3 Answers3

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The $-4\%$ would be the maximum decrease.

If you have $\$100$ and change it $-2\%$, you then have $100-0.02\times 100$ or $\$98$.

If you have $\$100$ and change it $-4\%$, you then have $100-0.04\times 100$ or $\$96$.

To deal with the sign, you could say "a change of $-4\%$" or "a decrease of $4\%$". They mean the same thing. (Just like "a change of $+4\%$" and "an increase of $4\%$" mean the same thing.)

John
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This is much more an English question than a mathematics one. Mathematically, $\max(-0.02,-0.03,-0.04)=-0.02$. When you ask about the "largest decrease" I would take the decrease to be a positive number and take the maximum of those, so a $4\%$ decrease is larger than a $2\%$ decrease. Whether you talk of percentages or absolute values does not matter to this.

Ross Millikan
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The formula to calculate percentage change is $$\frac{\textrm{new} - \textrm{old}}{\textrm{old}}\cdot 100%$$ where $\textrm{new}$ is the new value of the variable, and $\textrm{old}$ is the old.

So, using this formula, we can see that this expression is more negative if the difference between $\textrm{new}$ and $\textrm{old}$ is larger. Given that its negative, we know that $\textrm{new}$ is less than $\textrm{old}$. So, -4% is the maximum decrease.

For example, if $\textrm{old}$ is $100, \textrm{new}$ would be \$98 with -2%, \$97 with -3% and \$96 with -4%.

Rushabh Mehta
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