Math CentralQuandaries & Queries


Question from Asher:

Question: Is there an equation to find what percent of 0 is 1?

I remember learning quite a long time ago that the answer inst 0 and it isn't infinity. I'm pretty sure it was something like %=0 approaching infinity or %=1 approaching infinity. And I know it depends what value you assign the numbers i.e. dollars or temperature. Furthermore, is asking "what percent 1 dollar is of 0 dollars" the same question as "what percent profit do you make from selling something worth 0 dollars for 1 dollar."

Thank you for your time and consideration

Hi Asher,

Suppose the question was What percent of 12 is 3? The answer would be

\[\frac{3}{12} \times 100 = 25\]

so 3 is 25% of 12.

But the question is What percent of 0 is 1? Following the same procedure the answer is

\[\frac{1}{0} \times 100.\]

But division by zero is not a permissible operation so this expression is meaningless. There is no numerical answer to the question What percent of 0 is 1?

For your question about profit suppose you purchased an item for $\$9$ and you sold it for $\$12.$ Your profit is them $\$12 - \$9 = \$3.$ Profit, expressed as a percent is the profit as a percentage of the selling price. Hence in this case the profit is

\[\frac{\$3}{\$12} \times 100 = 25 \mbox{ or 25%.}\]

Hence if you purchased something for 0 dollar and sold it for 1 dollar you profit would be 100%.

I hope this helps,

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