To determine how close the two bounds of the interval should be for the method of bisection to provide an accuracy of within two decimal places, you need to consider the precision required for the root.

For an accuracy of two decimal places, the difference between the two bounds must be less than 0.01. In other words, if you denote the bounds as $a$ and $b$, you need:

$|b - a| < 0.01$

This ensures that the approximation for the root, which is usually taken as $\frac{a + b}{2}$, will be accurate to at least two decimal places.

If you need further details or explanations, feel free to ask! Here are some related questions you might consider:

1. How does the method of bisection work in finding roots?
2. What is the theoretical basis for the method of bisection?
3. How can I improve the efficiency of the bisection method?
4. What are the limitations of the bisection method?
5. Can you explain how to implement the bisection method in a programming language?

Tip: Always ensure that the function changes sign over the interval you are considering; this guarantees a root exists between $a$ and $b$.