To determine the error interval for $x$ rounded to two decimal places (15.31), follow these steps:

Key Concept:

When a number is rounded to 2 decimal places, the possible range (error interval) includes all values that would round to $15.31$. This range extends halfway to the next possible rounding value in either direction.

Calculation:

1. The rounding precision is $0.01$, so the error margin is $\pm 0.005$.
2. Lower bound: $15.31 - 0.005 = 15.305$.
3. Upper bound: $15.31 + 0.005 = 15.315$.

Error Interval:

The error interval for $x$ is: $15.305 \leq x < 15.315$

This ensures that $x$ includes all values that round to $15.31$ when rounded to two decimal places.

Do you have any questions or want further clarification?

Here are 5 related questions to deepen your understanding:

1. How would the error interval change if the number was rounded to 1 decimal place instead?
2. What is the general formula for finding the error interval for a number rounded to $n$ decimal places?
3. How does rounding to the nearest integer affect the error interval?
4. Can the error interval be expressed in other notations, like set notation?
5. How would you determine the midpoint of the error interval?

Tip: Always remember that the bounds of an error interval are symmetric around the rounded value!