Measured numbers and their significance are important topics. Here is an old exam question that requires application of these concepts.

A student measured the mass of 5 mL of a liquid to be 120.0 g. What is the density of the liquid (with proper attention to significant figures)?

Since a calculation is required to answer this question, we recommend solving the problem before looking at the possible answers. This way you can write out what you were given, jot down a formula, and solve the question before being "distracted" by possible answers.

(Note: sometimes students think that multiple choice questions can be answered by simply, "picking out the best answer" without performing the calculation. Rarely is this the case.)

Now that you have performed the calculation, look at the possible choices. Bummer, 24 is not an option. Hmmm. Think, think. Aha! Could the problem be significant figures? The calculator showed two digits in the display. Is that what I report? What's the meaning of the measured numbers used in the calculation? When multiplying, the reported answer can't have more significant figures than any of the original numbers (see rule #1 page 27 McMurry text). The volume only has one significant figure, so, the answer can only have one significant figure. This means I would want to round 24 to one sig. fig. and report 20 g/mL as my answer.

Now it is your turn. Let's start by taking some measurements.

Ruler #1 is divided into 1 centimeter increments. What is the length of the line using this ruler? How many significant figures are in this measurement?

Ruler #1

Use your measured length to calculate the area of a square with sides that are the length you determined. Example: if your answer above is 2.1 cm, the area of your square would be (2.1 cm)(2.1cm) = ___cm².

Report the area of the square using YOUR measurement.

Ruler #2 has additional divisions shown (0.1 cm increments). Report the length of the line using this ruler. How many significant figures are in this measurement?

Ruler #2

Use this measured length to calculate the area of a square with sides that are the length you determined.

Report the area of the square using this second measurement.

The length of the line was the same in both pictures. The difference was that one ruler had more divisions than the other. How did that impact the area you reported? Please explain.