Return to Metric Table of Contents
Problem #1a: Convert the speed of light (3.00 x 108 m/sec) to km/year.
Solution:
Doing this type of problem is simply a succession of conversions from one unit to another. You first convert one side of the fraction, then the other. We'll start with the numerator, since that's an easy, one step conversion.
This gives an answer of 3.00 x 105 km/sec.
Now, we have to focus on converting seconds to years. This is done in a step-by-step manner. For example, I happen to have memorized that there are 3600 seconds in one hour. So, we do that conversion.
Continuing the calculations, we move step-by-step to days and then to years (we can skip months, since we know how many days there are in a year.
Converting to scientific notation and rounding to three significant figures, we get 9.46 x 1012 km/yr as the answer.
Notes on variations of the above problem:
1) Notice that I used 365 days rather than 365.25. Using the latter figure results in an answer of 9.46728 x 1012 km/yr, which rounds off to 9.47 x 1012 km/yr.
2) This problem can start with cm/s rather than m/s. The speed of light in cm/s is 3.00 x 1010 cm/s.
23 Often, this problem ends in km/hr. Another common question asks for the conversion from cm/s to km/hr.
Problem #1b: Light travels at a speed of 3.00 x 1010 cm/s. What is the speed of light in kilometers/hours?
Solution:
1) Convert cm/s to km/s:
3.00 x 1010 cm/s times (1 m / 100 cm) times (1 km / 1000 m) = 3.00 x 105 km/s
2) Convert seconds to hours:
3.00 x 105 km/s times (60 s / 1 min) times (60 min / 1 hr) = 1.08 x 109 km/hr
3) A slightly more compact version:
3.00 x 1010 cm/s times (1 km / 105 cm) = 3.00 x 105 km/s3.00 x 105 km/s times (3600 s / 1 hr) = 1.08 x 109 km/hr
Problem #2: Convert 64.3 g/mL to its equivalent in kg/L.
Solution:
Convert grams to kilograms:
64.3 g/mL x (1 kg/1000 g) = 0.0643 kg/mL
Convert mL to L:
0.0643 kg/mL x (1000 mL/L) = 64.3 kg/L
Comment: teachers like to ask this type of question on tests. The ChemTeam did!
Problem #3:
A cylindrical piece of metal is 4.50 dm in height with radius of 5.50 x 10¯5 km.a) Calculate the volume in milliliters to the correct significant figures given V = π r2 h for a cylinder.
b) Calculate the volume in mm3
c) Calculate the density in units g/L to the correct number of significant figures given it has a mass of 6.54 x 105 grams
The key to solving part a is to remember that cm3 and mL are the same volume, so 1 cm3 = 1 mL. So, if we convert both measurements of the cylinder to cm, like this:
then, all we need to do is plug our numbers into the volume formula provided to get cm3.
I will leave you to solve parts b and c, however, the answer is here.
