Question

It was shown in the text that in a value such as 4000g, the precision of the number is uncertain. The zeros may or may not be significant.

a. Suppose that the mass was determined to be 4000g. How many significant figures are present in this measurement?

b. Suppose you are told that the mass lies somewhere between 3950 and 4050 g. Use scientific notation to report the value, showing an appropriate number of significant features.

Answer 1

a) Nobody knows. Any scientist who writes down a measurement like "4000 g" should have his degree taken away, then be tied to a stake and beaten with a rubber gas hose. You might as well write down your measurement in secret code, or in Roman numerals, because no one is going to know how to interpret the precision of your measurement.

b) This statement, too, is unscientific, because both the upper and lower limits are AGAIN given with ambiguous precision. Is the precision +/- 50. or +/- 5 x 10^1 ? Bah.

Assuming what you're trying to say is that this measurement is good to +/- 5 x 10^1 g, then you should write 4.00 +/- 0.05 x 10^3 g. You COULD write 4.0 x 10^3 g, and rely on the convention that the last sig dig could be off by as much as +/- 1, but if you actually know the precision you should always state it. Significant digits are just a quick and easy substittue for careful statements about precision, when you don't want to bother with (or don't know enought to make) the latter.

Answer 2

a.) there is only one sig fig in 4000

b.) you want the answer "to the nearest hundred." This would mean that the thousands and the hundreds place would be significant - 2 sig figs. If the actual number was out of the stated range, it would be closer to 3900 or 4100.

c.) \[4.0 \times 10^{3}\]

Answer 3

a) By the words of Walter Lewin: "Any measurement that you make without the knowledge of its uncertainty is completely meaningless."