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.

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.

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.