3

$n = 100$% of n

if $n=0$ then $0 = 100$% of $0$, but

$0 = 1$% of $0$, $0 = 2$% of $0, 0 = 3$% of $0$, etc

Is it correct to say that $0$ is not $100$% of $0$?

Maxim
  • 41
  • 100% is $1.0$ and 1% is $0.01$. We have $0= a \times 0$ for every $a$ and thus x% of $0$ is always $0$, whatever is $x$ (1 slice of no cake is no slice; 2 slices of no cake are no slices, etc.). – Mauro ALLEGRANZA Dec 20 '16 at 09:59
  • 0 = x% of 0 does not have a unique answer since this would require dividing by zero. – Florian Dec 20 '16 at 10:02
  • If your statement was incorrect, then 0 would be 100% of 0 - I think your statement is correct. – Cato Dec 20 '16 at 10:02

4 Answers4

6

By your reasoning, $4$ is not $1+3$ because $4$ is already $2+2$. Nope. $4$ is both $1+3$ and $2+2$, and of course many other things like $8 \div 2$.

user21820
  • 57,693
  • 9
  • 98
  • 256
  • The key is that we have many different expressions that refer to the same object. Given any decimal number $x$, the expression "100% of $x$" refers to the same number as $x$, and so we are always correct in writing "100% of $x$ = $x$". – user21820 Dec 20 '16 at 11:18
5

I think if you go this way, you may say : $0$ is not only $100\%$ of $0$.

Olivier Oloa
  • 120,989
2

There is a subtlety here not captured in the other answers. If we say that $a$ as a percentage of $b$ is $$\frac ab \times 100\%$$ then $0$ as a percentage of $0$ becomes $$\frac 00 \times 100\%$$Now $\frac 00$ is undefined, and in general we cannot divide by zero, so the percentage is strictly undefined. The subtlety is the division by zero which is concealed by the language about percentages.

The language about percentages is, to be sure, often used less formally than the defined operations of arithmetic. The extent to which this matters therefore depends on the formality of the context.

Mark Bennet
  • 100,194
  • 3
    The original phrasing means "100% $\times$ ..." so there is no division at all. Of course, one had better be aware of the subtlety that you point out when asking the question "How many percent of $b$ is $a$?" which is an ill-defined question if $b = 0$, regardless of $a$. – user21820 Dec 20 '16 at 10:37
1

Every percent of $0$ is $0$. So, no, it is not correct to say that. $0$ is $100\%$ of $0$.

MPW
  • 43,638