pamela uses a digital scale to find the mass of a rock fragment for her science class. the scale displays…

pamela uses a digital scale to find the mass of a rock fragment for her science class. the scale displays the fragments mass as 12.97 grams. the scale is only accurate to the nearest hundredth of a gram, so pamela knows that the rock fragment probably doesnt have a mass of exactly 12.97 grams. which of the following is the most appropriate range of possible values for the rock fragments actual mass? 12.95 to 13.00 grams 12.96 to 12.98 grams 12.969 to 12.971 grams 12.965 to 12.975 grams

pamela uses a digital scale to find the mass of a rock fragment for her science class. the scale displays the fragments mass as 12.97 grams. the scale is only accurate to the nearest hundredth of a gram, so pamela knows that the rock fragment probably doesnt have a mass of exactly 12.97 grams. which of the following is the most appropriate range of possible values for the rock fragments actual mass? 12.95 to 13.00 grams 12.96 to 12.98 grams 12.969 to 12.971 grams 12.965 to 12.975 grams

Answer

Explanation:

Step1: Understand accuracy to nearest hundredth

When a measurement is accurate to the nearest hundredth, if the measured value is $x = 12.97$ grams, the actual value $a$ lies in a range.

Step2: Determine lower - bound

The lower - bound is found by considering that if we are rounding to the nearest hundredth, the actual value could be just above the value that would round down to $12.96$. The value that rounds up to $12.97$ from the lower side is $12.965$ (since when we round $12.965$ to the nearest hundredth, we get $12.97$).

Step3: Determine upper - bound

The upper - bound is found by considering the value that would round down to $12.97$. The value that rounds down to $12.97$ from the upper side is $12.975$ (but we do not include $12.975$ itself when considering values that round to $12.97$ to the nearest hundredth). So the upper - bound is $12.9749\cdots\approx12.975$, and we can say the range is from $12.965$ to $12.975$ grams.

Answer:

$12.965$ to $12.975$ grams (but among the given options, the closest and correct one is $12.965$ to $12.975$ grams which is approximated by the option $12.965$ to $12.975$ grams as the correct range from the choices provided is $12.965$ to $12.975$ grams)