Ocean 001, Oceanography, satisfies the Natural Sciences - Mathematics (quantitative) general education requirement, so we expect that you to be willing to manipulate a few numbers during this quarter. We understand that some of you do not have a strong math background, and we will work with you throughout the quarter to understand difficult, quantitative concepts. In order for you to get a sense of our expectations, and for us to learn the level of the class as a whole, we have prepared these example questions. Please work through these examples and check with your instructor during one of our discussion sessions in lecture if you have any questions. I will let you know when to complete this assignment. We will post the solutions outside of my office door. You will not be graded on these questions! It is in your best interest to complete this exercise and let us know if there are parts that confuse you.
Unit conversion: See Appendix I, pp. 473-475 in T+T text. During this class we will deal with a wide array of units to discuss the size or weight or speed of objects. You will need to be able to convert between different unit types. Appendix I in the text contains tables with handy conversion factors. Here are a few examples:
Length: 1 mile = 5280 feet
1 foot = 0.3048 meters
Time: 1 day = 86,400 seconds
Mass: 1 kilogram = 2.2 pounds
1 metric ton = 2205 pounds
1. A. Convert 20,000 feet into miles.
B. Convert 20,000 feet into meters.
C. Convert one week into seconds.
D. Convert two tons into kilograms.
Temperature is measured using one of three common scale: Fahrenheit (°F), Celsius (°C), and Kelvin (K). You are probably most familiar with the Fahrenheit scale, but the Celsius and Kelvin scales are most useful in natural science. Here is how you convert between different scales:
2. A. Convert from 98.6 °F to °C (typical human body
temperature).
B. Convert from 212°F to °C (boiling point for pure water
at Earth's surface).
C. Convert from 0°C to °F (freezing point for pure water at
Earth's surface)
D. Convert from 0 K to °C ("absolute zero").
Fraction to decimal conversion: We are used to dealing with simple fractions like 1/2 pound or 1/4 mile, but in oceanography we will often want to convert these fractions into decimals. For example, the conversion of 1/4 to a decimal is found by dividing 1 by 4 = 0.25. This is particularly handy when working with maps, because maps are often divided up into degrees, minutes, and seconds of latitude and longitude. These are converted as follows:
1 degree (1°) = 60 minutes (60')
1 minute (1') = 60 seconds (60'')
We may need to convert units expressed in minutes and seconds into decimal degrees. For example, 23° 15' N (23 degrees, 15 minutes north) is equivalent to 23+(15/60) degrees = 23.25°.
3. A. Convert 45° 45' W into decimal degrees.
B. Convert 45° 35' W into decimal degrees.
C. Convert 45° 35' 28'' W into decimal degrees
(hint: first convert the seconds into decimal minutes, then
convert the total number of minutes into degrees and add these to
45).
Percentages and parts per thousand: One percent is one part per hundred (%). In oceanography, we will also talk about parts per thousand (ppt or o/oo).
4. 82% of oceanography students want to swim with porpoises. There are 150 oceanography students. How many oceanography students want to swim with porpoises?
5. 1000 g of seawater contains about 35 g of salt. Express the fraction of salt in seawater in percent and parts per thousand.
Metric multiples and submultiples: Within the metric system, there are common prefixes that indicate multiples of 10. For example: 1000 grams is a kilogram. On the other hand one thousandth of a gram is a milligram. Use the table in Appendix I to answer these questions:
6. How many grams are there in a megagram?
7. How many micrometers are there in a meter?
Length into area and volume: We will sometimes want to calculate the area or volume of an object based on its dimensions. Recall that for a rectangle, area is length times width (A = L * W). For a circle, the area is �r2, where � ~ 3.14. The volume of a box is length times width times height (V = L * W * H), while the volume of a sphere is 4/3�r3.
8. A frozen lake is 80 m long and 100 m wide. The surface of the lake forms a perfect rectangle. What is its surface area?
9. The ice on the lake is 0.3 m thick. What is the volume of ice on the lake?
Density: The density of an object or substance is expressed as the mass per volume. We may also talk about population density in terms of the number of objects per area or per volume.
10. The ice on the lake has a mass of 2160 kg. What is the density of this ice? [Hint: the units of density in this problem will be kg/m3.]
11. There are 80 people skating on the lake. What is the density of people, expressed as persons per area?
Rates: We will make use of rates throughout the class. One example of a rate is the speed of a car, often measured in miles per hour. We will generally use metric rates of motion: meters per second (m/s) or kilometers per second (km/s). Other rates might include the quantity of food consumed by a whale (in kilograms per day, kg/day) or the volume of water moved by a current (m3/s).
12. Mimi takes a trip from Santa Cruz, CA to Washington, DC (3,200 miles = 5,150 km). It takes her 12 days to make the trip. What is Mimi's average speed over the 12 days, expressed in miles/day and km/hr?
13. Andy is digging a hole in his back yard. After digging for 6 hours, the hole is 15 feet deep. What is Andy's rate of digging expressed in ft/hour and in m/s?
14. There are earthquakes on a fault every 5 years. Each earthquake moves the two sides of the fault away from each other by 0.5 m. What is the rate of movement across the fault in m/yr?
Text copied from UCSC, Earth 1 - Jim Zachos