The question is asking for the error interval of a number $x$ rounded to 2 decimal places, where $x = 7.19$.

When a number is rounded to two decimal places, the error interval represents the range of possible values that the number could have been before it was rounded. The general rule is:

• The lower bound is the rounded number minus half of the rounding unit.
• The upper bound is the rounded number plus half of the rounding unit.

Since the number is rounded to 2 decimal places, the rounding unit is $0.01$. Half of this unit is $0.005$.

Error Interval Calculation:

• Lower bound: $7.19 - 0.005 = 7.185$
• Upper bound: $7.19 + 0.005 = 7.195$

Thus, the error interval for $x$ is:

$7.185 \leq x < 7.195$

This is the range of values $x$ can take.

Would you like more details on this, or do you have any questions?

Here are five related questions you might find helpful:

1. How is the error interval affected by the number of decimal places?
2. How do you calculate the error interval for a number rounded to the nearest whole number?
3. What happens to the error interval if the number is rounded to more decimal places, e.g., 3 or 4 decimal places?
4. Can the error interval be applied to numbers rounded to significant figures?
5. How would you express the error interval for a negative number?

Tip: When calculating error intervals, always remember to add and subtract half of the smallest unit used in rounding.