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I was having a disagreement with a number of people commenting on a Daily Mail story and I got a few red arrows indicating disapproval to my comment that 35% is not a number but a proportion and that it is not 0.35 unless we are talking about 35% of 1. This derived from the following purported test question:

Arrange the following numbers from the smallest to largest:
a) 1/3
b) 0.305
c) 35%
d) 3/10

I argued that 35% is not a number but rather a proportion.

Not referencing the above test question but in general, is 35%=0.35 (not 35% of x but just 35% by its own)?

freethinker36
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  • x% is defined as x*1/100 – asddf Sep 07 '17 at 22:25
  • This is interesting. $35%$ does depend on what it is a percentage of, as you say. So $35%$ could be $0.35$ or $35$ if we are looking at a percentage of $1$ or $100$, respectively. However, without any context as to what the percentage is of, as in the context of the question highlighted (in yellow) above, it means that $35%$ is a percentage of $1$, so it would be considered $0.35$. – Dave Sep 07 '17 at 22:26
  • The fact that a percentage is really just a number divided by 100 became extremely clear to me when taking probability. Being able to say that "A happens with probability $0.5$" is a bit of an eye opener. We commonly use percentage to indicate a proportion like you said, but we also commonly use percentages in such a way that has nothing to do with proportions. – Kaynex Sep 07 '17 at 22:45

2 Answers2

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The symbol % means "per cent". In this case, "cent" means $100$, so % means $/100$.

35% means $35/100$ or $0.35$.

We often multiply percents by other quantities, like 80% of 200. Here, "of" designates multiplication. In the Daily Mail story there is no "of", so no multiplication and no ambiguity.

vadim123
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  • But what if there are 35 people selected from 100? That's not 0.35. – freethinker36 Sep 08 '17 at 17:15
  • @freethinker36, 35 people selected from 100 is 35% OF the total people. When a percentage is OF something, then we multiply. However a percentage can have meaning by itself, as in this case. – vadim123 Sep 08 '17 at 19:31
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In this context, a percent is a number just like the others.

So $35\% = 0.35$; it's the largest of the four.

John
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