To find the error interval for the number $x$ when rounded to 6.7 to one decimal place:

• The number $x$ could be slightly less than 6.7 but still round up to 6.7, or it could be slightly more than 6.7 but still round down to 6.7.
• The smallest possible value of $x$ would be 6.65, because rounding 6.65 up gives 6.7.
• The largest possible value of $x$ would be just under 6.75, because rounding 6.75 would give 6.8.

Thus, the error interval is:

$6.65 \leq x < 6.75$

Would you like further explanation on rounding intervals or have any other questions?

Here are 5 related questions:

1. What is an error interval in mathematical terms?
2. How do we calculate error intervals for different decimal places?
3. Can an error interval be expressed differently?
4. How do upper and lower bounds affect rounding?
5. What happens when a number falls exactly on the boundary of an interval?

Tip: When working with error intervals, always consider both the upper and lower bounds to understand the range within which the true value lies.