# Percentage nature [closed]

In mathematical expressions, the internationally recognized symbol % (percent) may be used with the SI to represent the number 0.01. Thus, it can be used to express the values of dimensionless quantities. According to Le Système international d’unités/The International System of Units, (Brochure sur le SI/SI brochure), 2006.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", or the abbreviations "pct.", "pct"; sometimes the abbreviation "pc" is also used.[1] A percentage is a dimensionless number (pure number). Based on Wikipedia, https://en.wikipedia.org/wiki/Percentage

Is percentage considered as a number?, e.i. can I add a number to percentage?

Which is correct

30+10%=30.1

or

30+10%=33

• This question doesn't seem to be about teaching mathematics and it would be more appropriate to ask at math.stackexchange.com Dec 19 '16 at 9:22
• @AmyB, I already asked it there, my intention to post it here is to know educators' perspective when they teach something like this. Dec 19 '16 at 11:30
• To those voting to close this question, the OP originally posted it at Mathematics Stack Exchange and I suggested that he repost it here, hoping that it would get a better reception. Dec 19 '16 at 13:04
• Ali Tarek, if you are interested in how mathematics educators translate the expression $30+10\%$, consider editing your question to something like "Is the addition of pure numbers with percentages taught in school? If so, then how is it to be interpreted?" Dec 19 '16 at 13:07
• I would take 30 + 10% to be an informal shorthand for 110% of 30 or $1.10 \times 30 = 33$. Dec 20 '16 at 15:29

## 2 Answers

This is a hard question to answer formally, but an easy question from an educator's perspective: it is very unlikely that adding a pure number and a percentage is a good idea. While a percentage has the same units as a pure number, they're usually represent different types, so adding them is unlikely to give a meaningful quantity. Anyone who finds themselves doing this should probably stop and ask themselves what led them there, and what the combined quantity is supposed to mean.

Unit analysis is as far as most classes get into the details of the typing rules of written mathematics, and the connection of those rules to meaningful computations, but teachers should always be modeling good practice.

Correct one: 30+10%=30.1

Corrected one: 30 * 110%=33

Percentage means exactly as you say. 1% = 0.01. It has a few versions: https://en.wikipedia.org/wiki/Percent_sign , permille ‰ is often used for alcohol content in blood. The per-cent means per hundred and per-mille per thousand. Because it is a shortening, it requires always a number front of it. % + % * 5 + %$^2$, would not be acceptable.