Percent sign after a fraction? Convert to percent Isn't it wrong to write the following with only the percent sign? Instead of $100 \%$?

The change in height as a percentage is
$$
\frac{a - b}{a} \% \tag 1
$$
where $a$ is the initial height and $b$ is the final height.

Because if $a=10$, $b=5$ we have
$$
\frac{10-5}{10}\%=\frac{1}{2} \% = 0.5 \frac{1}{100} = 0.005
\quad \text{what?!}
\tag 2
$$
If we convert a decimal number to percent we multiply it by $100$ and add the percent sign. We have $1\%=\frac{1}{100}$, so with $100 \%$ we multiply the number by $1$, i.e.
\begin{align}
\frac{10-5}{10} \cdot \color{blue}{1}
&=
\frac{10-5}{10} \cdot \color{blue}{100 \%}
=
\frac{5}{10} \cdot 
\color{blue}{100 \frac{1}{100}}
=\frac{1}{2} \cdot 
\color{blue}{100 \frac{1}{100}} \tag 3
\\
&=0.5\cdot \color{blue}{100 \frac{1}{100}}
=50 \color{blue}{\frac{1}{100}} = 50 \color{blue}{\%} \tag 4
\end{align}
So, shouldn't we instead write $(1)$ as
$$
\frac{a - b}{a} 100 \% \quad ? \tag 5
$$

Caution: some authors improperly write expressions like $\dfrac{a-b}a\%$ with the meaning that the value should be thought of as percents. In this case, the percent sign should not be taken for a factor. $\dfrac{a-b}a(\%)$ would be safer.
Leaving this on the side, IMO $$\dfrac{a-b}a\%$$ should rarely occur because there are no common reasons to multiply a fraction by one percent (if this really occurred, I would certainly write $0.01$ instead of $\%$). On the opposite, an evaluation like
$$\frac{a-b}a=5\%$$ makes perfect sense.
I also think that $$\dfrac{a-b}a100\%$$ is ugly/superfluous and would puzzle people.
