Using tables, find the value of (5/2.234)3.

The reciprocal of 2.234 is $\frac{1}{2.234}$.

$$\frac{1}{2.234} \approx 0.44762757$$

Let $N = \left(\frac{5}{2.234}\right)^3$.
We can write this as $N = \left(5 \times \frac{1}{2.234}\right)^3$.
Using logarithms:

$$\log N = \log \left(\left(\frac{5}{2.234}\right)^3\right)$$ $$\log N = 3 \log \left(\frac{5}{2.234}\right)$$ $$\log N = 3 (\log 5 - \log 2.234)$$

Using logarithm tables (or a calculator for precision):

$$\log 5 \approx 0.69897$$ $$\log 2.234 \approx 0.34909$$

Substitute these values:

$$\log N = 3 (0.69897 - 0.34909)$$ $$\log N = 3 (0.34988)$$ $$\log N = 1.04964$$

$$N = 10^{1.04964}$$ $$N \approx 11.2100$$

The first four significant figures are $1, 1, 2, 1$.

$$N \approx 11.21$$

The reciprocal of 2.234 is approximately 0.4476.
The value of $\left(\frac{5}{2.234}\right)^3$ to 4 significant figures is $\boxed{\textbf{11.21}}$.