Question

An object was carefully weighted on three different balance. Each balance was zeroed before weighing. The mass were: 10.35g, 10.335g, and 10.30g.calculate the average value of these measurement.(please show all work and pay attention to significant figure rules)

Answer 1

The average of the measurements 10.35g, 10.335g, and 10.30g, considering the rules of significant figures, is 10.33g. This is calculated by summing the individual masses and dividing by the number of measurements, then rounding to the same number of decimal places as the least precise measurement.

Step-by-step explanation:

To calculate the average value of the three measurements, we first add the masses together:

10.35g + 10.335g + 10.30g = 30.985g

Next, we divide the sum by the number of measurements (which is 3 in this case) to find the average:

Average mass = 30.985g ÷ 3 = 10.328333...³ g

According to the rules of significant figures, the average value should be reported with the same number of decimal places as the least precise measurement. Our least precise measurement is 10.30g, with a precision to the nearest hundredth (two decimal places). Thus, we round our average mass to two decimal places:

Average mass = 10.33g

The average value of the object's mass, taking into account significant figures, is 10.33g.