The problem asks for the error interval for the number $x$, which is rounded to 2 decimal places and is given as 7.38.

Solution:

When a number is rounded to two decimal places, the actual number lies within an interval. This interval is defined as:

$x = 7.38 \pm 0.005$

Error Interval:

• The lower bound of the interval is:
  $7.38 - 0.005 = 7.375$

• The upper bound of the interval is:
  $7.38 + 0.005 = 7.385$

However, since 7.385 would round to 7.39, the interval must exclude 7.385. Therefore, the error interval for $x$ is:

$7.375 \leq x < 7.385$

This interval represents the possible values of $x$ before rounding.

Would you like more details or have any questions? Here are 5 related questions to consider:

1. How is the error interval calculated when rounding to 3 decimal places instead of 2?
2. What is the general formula for determining the error interval for rounding to any number of decimal places?
3. Can the error interval concept be applied to significant figures as well?
4. What happens to the error interval if the number was rounded to the nearest whole number?
5. How can error intervals help in understanding the accuracy of measurements in scientific experiments?

Tip: When working with rounding errors, always remember that the interval is inclusive of the lower bound but exclusive of the upper bound to avoid over-rounding!