Final answer:
The place value of the underlined digit in 0.506 depends on which digit is underlined. It could be tenths, hundredths, or thousandths, resulting in rounded values of 0.50, 0.51, or 0.506 respectively.
Step-by-step explanation:
The question involves finding the place value of the underlined digit in the number 0.506 and rounding that number to the place of the underlined digit. Since the underlined digit in question is not specified, we will have to make assumptions. If the underlined digit is 5, its place value is tenths, meaning the number is rounded to 0.50. If the underlined digit is the first 0, its place value is hundredths, so the number is rounded to 0.51 since the next digit (6) is greater than or equal to 5 and we should round up. If the underlined digit is the last 6, its place value is thousandths, but since it's the last digit, the number would stay as 0.506 but could be considered to have a value of 0.006 in terms of thousandths alone. When rounding to a certain decimal place, we usually look at the digit immediately to the right of the target rounding place to decide whether to round up or maintain the current value. For example, when we want to round 201.867 to the hundredth place, since the first number being dropped is 7, we round up and report a final answer of 201.87.