To find the error interval for $x$, which is rounded to 3.4 to 1 decimal place, follow these steps:

When a number is rounded to 1 decimal place, the true value of the number lies within $\pm 0.05$ of the rounded value. This means:

• The lower bound is $3.4 - 0.05 = 3.35$.
• The upper bound is $3.4 + 0.05 = 3.45$.

However, the upper bound is not included because it would round to 3.5 instead of 3.4, so we write it as an inequality:

$3.35 \leq x < 3.45$

This is the error interval for $x$.

Would you like more details or have any questions about this solution?

Here are 5 related questions:

1. What would be the error interval if $x$ were rounded to 2 decimal places instead of 1?
2. How would you determine the error interval for a number rounded to the nearest integer?
3. If $x$ was rounded to 3.4 but the original number was 3.38, is it within the error interval?
4. Why is the upper bound in the error interval not inclusive?
5. How does the concept of significant figures relate to rounding and error intervals?

Tip: When determining error intervals, always remember that the lower bound is inclusive and the upper bound is exclusive for the given rounding precision.