Tricky math problem

Question

Gemstones are measured in carats (CD), with a carat having a mass of 200.0 milligrams.

A unit of area used in nuclear physics is the barn (b). One barn equals 1 x 10^-28 m², a typical nuclear cross section.

You probably know the following units of length: one yard (yd)= 3 feet (ft), one foot (ft)= 12 inches (in), one inch = 2.54 cm.

Bugs Bunny wishes to convert the density of water from one gram/cm³ to carats/barn*yard

What value should he find? (4 marks)

Answer 1

Hi Alex J.,

What a cute verbal joke. But how you solve it is exceedingly simple. Start by writing the starting value:

1 g / cm^3 . Next, start multiplying this by conversion factors. A conversion factor is a ratio of two things that are physically equal, but have different numeric values because they have different units. An example might be: 1 carat / 200 mg . Also, 1000mg / 1 g .

Do you see how each of these expressions represents the same physical thing in the numerator and denominator, but the units are different? When you multiply these 3 expressions together, and cancel out units, you should end up with: 5 carat(s) / cm^3 . Now you have to do the same to replace the units in the denominator (cm^3) with the units you need in the final form. Again, you use conversion factors. Note that you need one multiplication to insert the /barn , and another to insert the /yard . I'll leave the labor of that up to you! Strategy tip: convert first to / m^3 , then work by separating that first into / (m^2 * m) , etc.

-- Cheers, --Mr. d.