To solve this problem, we need to find the error interval for $h$, given that $h$ is rounded to two significant figures and is equal to 0.072.

Step 1: Identify the range for two significant figures

The number $h = 0.072$ is rounded to two significant figures. The lower and upper bounds for $h$ will be based on how the number might round to 0.072.

Step 2: Calculate the lower and upper bounds

When rounding to two significant figures, we consider the halfway points that would still round to 0.072:

• Lower bound: The smallest number that would round up to 0.072 is halfway between 0.071 and 0.072. That number is: $\text{Lower bound} = 0.0715$
• Upper bound: The largest number that would round down to 0.072 is halfway between 0.072 and 0.073. That number is: $\text{Upper bound} = 0.0725$

Step 3: Write the error interval

Thus, the error interval for $h$ is: $0.0715 \leq h < 0.0725$

This represents the range of possible values for $h$ that would round to 0.072 when rounded to two significant figures.

Do you have any questions or would you like further details?

Here are some related questions to expand your understanding:

1. How is the error interval affected when rounding to different significant figures?
2. Can error intervals be applied to numbers rounded to decimal places instead of significant figures?
3. How do you calculate an error interval for larger or smaller numbers (e.g., 700 rounded to 2 sig. figs.)?
4. What is the difference between rounding to significant figures and rounding to decimal places?
5. How would the error interval change if the number was rounded to 1 significant figure?

Tip: Always remember that for significant figures, the bounds are calculated by finding the halfway point between possible rounded values.