Question

Suppose that a series of measurements have shown that the mean mass of an object is 122.4g with

deviation of 1.3 g. How many significant figures are justified in the mean and how would you report the
most probable mass of the object? Explain.

Answer 1

The mean mass of the object, 122.4g, justifies four significant figures, with the most probable mass reported as 122.4 grams, in line with the precision of the measurements.

Step-by-step explanation:

When considering the number of significant figures justified in the mean mass of an object reported as 122.4g with a standard deviation of 1.3 g, we look at the precision of the measurements. The mean mass has four significant figures (1, 2, 2, and 4) because each of these digits contributes to the value's precision. The decimal place in the standard deviation (1.3) suggests it is precise to the tenth of a gram, reinforcing that the mean mass reported is to a similar precision.

Therefore, the most probable mass of the object should be reported as 122.4 grams, consistent with the precision of the measurements taken. This reporting reflects a clear result of measurement while respecting the significant figures rule for addition and subtraction, where the answer must match the least precise measurement. Note that if the measurement were 122.0g, this would pose uncertainty unless expressed in exponential notation.

Answer 2

• How many significant figures are justified in the mean: three significant figures.

• How would you report the most probable mass of the object: as 122 which is 122.4 rounded to three significant figures.

Step-by-step explanation:

If the deviation is 1.3 g the true measurement will be within the interval 122.4g - 1.3g to 122.4g + 1.3g:

• Lower limit: 122.4 g - 1.3 g = 121.1 g

• Upper limit: 122.4 g + 1.3 g = 123.7 g

Hence, only the first two digits, hundreds and tens places, are certain. The ones digit is uncertain.

Since, the signficant figures include the certain digits plus one uncertain digit, you should report the number with three significant figures: 2 certain digits + 1 uncertain digit.

The most probable mass of the object would be the mean which is 122.4, which must be rounded to three significant figures, i.e 122 g.