To find the error interval for the number $n$, which is rounded to two decimal places and results in 3.87, let's consider how rounding works:

When a number is rounded to two decimal places, the third decimal place determines whether the number rounds up or stays the same.

• If the third decimal place is 5 or higher, the number rounds up.
• If the third decimal place is less than 5, the number stays the same.

So, the number $n$ must lie between 3.865 and 3.875 (since 3.87 is the rounded result):

$3.865 \leq n < 3.875$

Thus, the error interval for $n$ is:

$3.865 \leq n < 3.875$

Would you like any further explanation or more examples? Here are some related questions:

1. How do we determine rounding intervals for other decimal places?
2. What happens when the rounding is done to the nearest whole number?
3. How can we apply this concept to real-world measurements?
4. What if the rounding was to three decimal places instead of two?
5. How does rounding affect statistical data analysis?

Tip: When rounding to any decimal place, always look at the digit in the place immediately following the rounding place to decide whether to round up or not.