Question

An object was carefully weighed on three different balances. Each balance was zeroed before weighing. The masses were: 10.35 g, 10.355 g, and 10.30 g. Calculate the average value of these measurements. (Please show all work and pay attention to significant figure rules.)

A) 10.34 g
B) 10.357 g
C) 10.33 g
D) 10.36 g

Answer 1

To find the average mass, sum the three masses (31.005 g), divide by 3 to get 10.335 g, and round to the same decimal place as the least precise measurement, yielding 10.33 g as the correct average.

Step-by-step explanation:

The question involves calculating the average mass of an object based on three different measurements while paying attention to the rules of significant figures. The measurements provided are 10.35 g, 10.355 g, and 10.30 g.

To find the average, we add the three measurements and divide by 3, but we have to consider the least precise measurement when doing so.

First, we calculate the sum of the masses: 10.35 g + 10.355 g + 10.30 g = 31.005 g.

Next, we divide this sum by 3 to get the average: 31.005 g / 3 = 10.335 g.

However, our least precise measurement is 10.30 g, which is accurate to the hundredths place.

Therefore, the average mass must be reported to the same decimal place, and hence it should be rounded to two decimal places, resulting in 10.33 g as the correct average mass.