To find the error interval for $x$, which is rounded to 7.19 to 2 decimal places, we need to determine the range of values that round to 7.19 when rounded to two decimal places.

1. Identify the midpoint: The midpoint is 7.19.

2. Determine the rounding bounds: To find values that would round to 7.19, we go 0.005 above and below this value.

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

3. Write the error interval: Since 7.195 would round to 7.20 if rounded, we include the lower bound and exclude the upper bound.

   $7.185 \leq x < 7.195$

This interval represents the range of values that would round to 7.19.

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Related Questions:

1. What would be the error interval for a number rounded to 7.20?
2. How do we determine error intervals for numbers rounded to different decimal places?
3. What would the interval look like if the number was rounded to one decimal place instead?
4. Why do we exclude the upper bound in this type of error interval?
5. How can we express error intervals for numbers in scientific notation?

Tip:

Always remember, the error interval is found by adding and subtracting half of the smallest unit based on the decimal place to which the number is rounded.