## Quiz: Measurement and dimensional analysis.

Cracolice 2/e Ch 3.

Abbreviations: CF = conversion factor(s); PT = periodic table; SF = significant figure(s).

Quiz is "closed book" except for PT & calculator. If a question requests an explanation, there may be no credit unless you have provided an explanation.

1.
a. Which is bigger, a millimeter (mm) or a meter (m)?

b. How many times bigger?

c. Using your answers from parts a and b, write a conversion factor between mm and m.

2. You measure the length of an object, and record it as 65.6 cm (centimeters).

a. Convert this measurement to meters. 100 cm = 1 m. Use the method of dimensional analysis; show clear work. The problem will be scored primarily based on the clarity of your work.

b. A meter is (bigger OR smaller) than a centimeter. Therefore, the measurement in meters should be a (bigger OR smaller) number than the measurement in cm. [In each sentence, choose the proper term from the parentheses.]

** Check to see if your answers are consistent... Does your result in part a agree with what you predict here in part b? If not, something is wrong! (A check such as this can protect you against some silly mistakes, and can also sometimes serve as a warning flag that you do not quite understand an idea.)

3. If the density of one marble is 2.5 g/cm3, what is the density of four marbles? Explain or show work.

The following two questions (#4-5) are intended to stretch you a bit on handling units. Both involve simple equations; one is familiar (in your chem book), and the other -- much in the news -- is given in the question. At least some parts require extensive unit conversions.

4. Obesity is much in the news. One criterion to measure obesity is the BMI (= body mass index). The BMI is the ratio of your mass to the square of your height, in the metric units kg/m2. (BMI = 25-26 is "borderline overweight".)

a. Calculate the BMI for a person, 2.0 meters tall, weighing 80 kg.

b. Calculate the BMI for a person, 5 feet 7 inches tall, 156 pounds. See your textbook for the conversion factors.

5. The Cassini spacecraft is making measurements of Saturn and its moons. This question is based on information about Enceladus, a moon of Saturn. Assume that it and other bodies mentioned are spherical.

a. An author made a comparison between Enceladus and Triton (a moon of Neptune). He said that Triton's diameter is 5 times that of Enceladus, and its mass is 200 times that of Enceladus. How much denser (how many times as dense) is Triton than Enceladus? Explain.

b. The mass of Enceladus is 1.08x1020 kg, and its radius is 252.1 km. Calculate the density of this moon. (The formula for density of a sphere is given in the answer key, for part a.) You can give the answer in any convenient units, but also give it in g/mL (g/cm3), which you will need for part c.

c. Someone suggests that Enceladus is made almost entirely of ice (i.e., ordinary water ice). Is the density of this moon consistent with that suggestion? Explain.

6. Calculate 2.67x1019 * 4.336x10-8 * 1025, using your scientific calculator. Report the proper number of SF, assuming that the first two given numbers are based on experimental measurements.

The purpose of the question is to see whether you know how to use the scientific notation keys on your scientific calculator. The only general way (which will work on all scientific calculators) to enter exponents is with the "enter exponent" key. Using keys such as yx, 10x, or typing the "10" represents improper use of the calculator for this purpose, and often leads to incorrect answers. Entering 1025 will require that you find out whether your calculator requires a leading 1.

(The details of how to use scientific notation are somewhat different with different calculators. Your calculator may allow other procedures. But if you pick up an unfamiliar scientific calculator, the proper way to proceed is with the method that works generally.)

All of the issues raised here are dealt with on the calculator worksheet that is handed out in class, or available here on the Using your scientific calculator page.

Last update: April 19, 2019