If a circle has radius less than one, does it mean that the circumference of the circle is bigger than the area? How can that even be possible?
For example, if a circle has radius $0.5$, then the circumference is $2 \pi \cdot 0.5 = \pi$, and the area will be $\pi \cdot 0.5^2 = 0.25 \pi$. How can this be the case?
On
As mentioned above, the units can have an affect on the ratios
For circumference of a circle $C=2\pi r\quad$ for area $A=\pi r^2\quad$ for ratio $$R=C/A=\frac{2\pi r}{\pi r^2}=\frac{2}{\pi r}\quad \land\quad r=1\implies R=\frac{2}{3.14\cdots}\approx 0.64$$
Management says the measure was in yards but should have been in feet
$$r=3\implies R=\frac{2}{3.14(3)\cdots}\approx 0.21$$
Management now says it WAS feet and should have been in yards $\quad (1/3$ that of feet)
$$r=1/3\implies R=\frac{2}{3.14(1/3)\cdots}\approx 1.91$$
So yes. If your radius is less than one, circumference can be larger than area.
You are comparing apples to oranges. Using the metric system, the circle has radius $r \text{ cm}$, while the circle has area $\pi r^2 \text{ cm}^2$. You can use the imperial system with $\text{in}$ and $\text{in}^2$, and they are still different units.
The units for length and area will always be different.
And what's wrong with an area smaller than $1$? If a square has area $0.25$, that means that its area is $0.25$ smaller than a square with area $1$. If I measure the area of your home in $\text{km}^2$, unless your home is $1 \text{km}$ by $\text{1 km}$, then your home will have an area smaller than $1 \text{ km}^2$.