1_skills review

Lab 1. Skills Review NAME________________________________ A few notes:  You do not need to submit this lab worksheet. Work through the worksheet first, then complete the Lab 1. Skills Review Quiz on the course Canvas page to get points.  Note that questions that are worth points have their points value highlighted in yellow.  Lab materials: Calculator, Ruler, Colored Pencils, Pen/Pencil, Camera/Scanner, Computer Review the following material in preparation for the lab. It helps to watch the videos provided on the course Canvas page, too. Units Watch the units and dimensions video on Canvas for more help. Table 1. Units of Length (distance) mm millimeter 10 mm = 1 cm cm centimeter 100 cm = 1 m m meter 1000 m = 1 km km kilometer 1 km = 0.6214 mi in inches 12 in = 1 ft ft feet 5280 ft = 1 mi mi miles 1 mi = 1.6093 km Table 3. Units of Time 1

s seconds 60 s = 1 min min minutes 60 min = 1 hr hr hours 24 hr = 1 day yr years 365 days = 1 yr Ma mega annum 1 Ma = 1,000,000 yr Ga giga annum 1 Ga = 1,000,000,000 yr Table 2. Units of Mass (weight) mg milligram 1000 mg = 1 g g gram 1000 g = 1 kg kg kilogram - lb pounds - Table 4. Units of Temperature 2

Known value in current units = Conversion factor in desired units Conversion factor in current units Example of basic unit conversion: Convert 3.5 years to days  3.5 years = 365 days = 1300 days 1 year Example of converting part of a unit of rate: Convert 0.0000002 m to m  0.0000002 m = 60 s  60 min  24 hr  365 days = 6 m/yr s yr s 1 min 1 hr 1 day 1 yr Example of converting squared value: Convert 2.5 mi 2 to km 2  2.5 mi 2 = 1.6 km  1.6 km = 6.4 km 2 1 mi 1 mi Useful Equations Area = width  length (in units of length squared, ex. km 2 ) Volume = width  length  height (in units of length cubed, ex. km 3 ) Density = mass  volume (in units of mass divided by length cubed, we will use g/cm 3 in this course) Velocity (or Rate) = distance  time (in units of length divided by time, ex. m/s) Exercise 1. Significant Figures Reporting calculations in the correct number of significant figures prevents you from overstating the precision of your data. See the example below and the video on Significant Figures on Canvas for help. Here’s an example: Calculate the average age of Earth Science Instructors, Tram (34), Cara (37) and Ixchal (33). 34 + 37 + 33 = 34.66666666666666667 years (equation 1) 3 BUT, do we really know their age to that precision? Is Tram exactly 34.0000000000000000 years old? Is Cara exactly 37.0000000000000000 years old and Ixchal exactly 33.0000000000000000? The answer is NO. For this reason, the answer written above overstates the precision of our data (instructor ages) and we need to count the correct number of significant figures. Here are the rules for counting significant figures:  Non-zero digits are always significant (ex: the numbers 7864 and 7864000 both have four significant figures)  Any zeros between non-zero digits are significant (ex: 1020 has three significant figures)  A final zero to the right of a decimal point is always significant (ex: 1.0 has two significant figures).  Zeroes to the left of a decimal point are also significant (10. Has two significant figures, 10.0 has three). An exception is if the zero doesn’t have a sig fig to the left of it (EX: 0.1 only has one significant figure) How do I decide how many digits to report my answer in?  Choose the lowest number of significant figures in your data and report your 4

 Do not consider significant figures for conversion factors if you’ve converted units. (ex 1 mile = 5280 feet – don’t worry about the number of sig figs in either number).  Reporting answers in the correct number of significant figures is not about how many digits are past the decimal, it’s about counting the total sig figs in your answer. Let’s go back to equation 1 above (the average age of our instructors). Since our lowest number of significant figures in our data (34, 37 and 33) is 2, our answer should be reported in two significant figures. The average age of our instructor is 35, not 34.66666666666666667. (a) How many significant figures are in the following numbers? ( 3 pts) 455,000,000,000 ____________ 0.00000016 ____________ 0.000000160 ____________ 2.00017 ____________ (b) Calculate the average salary of my colleagues in geosciences. Emily earns 183,000/year, Dimitri earns 135,000/year and Jeremy earns 91,000/year. Report your answer in the correct number of significant figures ( 3 pts) Exercise 2. Scientific Notation Scientific notation is a way to easily write very large or very small numbers. See the example below and watch the Scientific Notation video on Canvas for help. Here are the rules for very large numbers:  For very large numbers, count the number of digits to the right of the first digit (ex: there are six digits to the right of the two in 2,500,000).  Move the decimal place to the left so that it is to the right of the first digit and add the notation x10 # of digits (ex: 2,500,000 = 2.5x10 6 ). Rules for very small numbers:  For very small numbers, count the number of digits that come after the decimal point up to the first significant digit (ex: there are six digits to the right of the decimal point in 0.0000051).  Move the decimal point so that it is to the right of the first digit and add the notation x10 -# of digits (ex: 0.0000051 = 5.1x10 -6 ). Basically, you are counting the number of times the decimal point “jumps”. If it jumps to the left (for big numbers) your notation is positive (x10 6 ) and if it jumps to the right (for small numbers) the notation is negative (x10 -6 ). NOTE: ONLY USE SCIENTIFIC NOTATION WHERE PRACTICAL!!! (a) Write the following values in scientific notation with only one digit to the left of the decimal (similar to the examples in the video on Canvas): ( 3 pts) 455,000,000,000 _______________ 0.00000016 _______________ 0.00251 _______________ 2000 _______________ 5

(e) Ok, let’s now think about the growth rate of mountains! The Andes Mountains started forming approximately 8 million years ago (or 8 mega-annum (Ma); see Table 3). Since that time, Mount Aconcagua (the highest peak in the Andes) has grown to 3.962 km high. Calculate the growth rate of the Mount Aconcagua in km/Ma (kilometers per mega-annum). *Note: Be careful with units here – you’re calculating in km/Ma, NOT km/year! ( 3 pts) (f) How many significant figures should you answer for question (e) be reported in in order to accurately represent the precision of your data? ( 1 pts) (g) The answer for question (e) is difficult to comprehend since we don’t know what a million years feels like. We do know what a year feels like, though! Use the space below to convert your answer to mm/yr. ( 3 pts) (h) Now let’s think about something that moves fast instead of very slow. Earthquake waves are energy waves that move through rock and along the surface of the Earth. The fastest type of earthquake waves travel approximately 4800 meters per second in granite (a rock type we will talk about later in the semester). What is the velocity of these earthquake waves through granite in miles per second? Be sure to refer to the video on unit conversions provided on Canvas. ( 3 pts) (i) Let’s say that the 1994 earthquake originating in Northridge was felt in Phoenix. Given the rate you calculated in question (h), how long would it have taken for the fastest earthquake waves to travel between these two cities? Assume the waves are traveling through granite only and the distance between LA and Phoenix is 380 miles. Express your answer in minutes. ( 3 pts) 7

Hint: Rate = Distance  Time. The question asks for time (how long), so solving for time gives you: Time = Distance  Rate Exercise 4. Calculating density of materials Watch this video, which provides a demonstration of how to calculate density of an irregularly-shaped object, like a rock sample: https://www.youtube.com/watch?v=ovdE_-FCWpc . *Note “cc” = cubic centimeter (cm 3 ). (a) What two measurements/variables are required to calculate the density of an object? ( 2 pts) (b) What are the units of density that we will use in this course? Hint: look at the “Useful Equations” section of this handout. ( 2 pts) (c) Graduated cylinders usually measure fluids in units of milliliters (ml). Given the explanation in the video provided, 1 ml of water has a volume of approximately 1 ______ at surface temperature. ( 2 pts) (d) A rock sample that weighs 450 g and displaces water by 150 ml has a density of: _____________ ( 3 pts) (e) Will this rock sample you determined the density for in question (d) sink or float in water, which has a density of 1 gram/cm 3 ? _____________ ( 1 pts) (f) A rock sample that weighs 100 g and displaces water by 200 ml has a density of: _____________ ( 3 pts) (g) Will this rock sample you determined the density for in question (f) sink or float in water, which has a density of 1 gram/cm 3 ? _____________ ( 1 pts) Exercise 5. Plotting changes within Earth’s crust Here you will to plot how temperature changes with depth in Earth’s crust. The rate of change of temperature with depth is called the geothermal gradient (“geo” = Earth, “thermal” = temperature and “gradient” = change. Keep these things in mind while plotting:  The y-axis (vertical) will represent increasing depth below the surface (so start with 0 km at the upper left). 8

(d) Rock pressure in Earth’s crust also increases with depth. This is called geobaric gradient (“baric” = pressure). The average increase in pressure with depth is 1 kilobar (kb) for every 3 kilometers depth. Using this information, print a separate plot (provided on the next page) and draw a line representing the average geobaric gradient (it doesn’t matter what color you use  ). ( 5 pts) Some notes:  Don’t forget to label the x-axis so your line actually means something.  Start at 0 kilobars of pressure on your x-axis and 0 km depth on your y-axis.  Again, you will upload this plot to Canvas, so make sure you take a good image/scan of the plot. Your file should be a pdf, jpg, png or heic.  Include your name (hand-written) on the printed plot, draw your line with a ruler, and only upload the geobaric gradient plot, NOT your entire lab. Geobaric Gradient 10

(e) Using your geothermal gradient plot, what is the possible range of crustal temperatures at 2 km depth? ( 2 pts) (f) Using your geothermal gradient plot, what is the possible range of crustal temperatures at 5 km depth? ( 2 pts) (g) Using your geobaric gradient plot, what is the average pressure at 5 km depth? ( 2 pts) Exercise 6. Scientific Method Read the passage below and answer the corresponding questions: Geologist Ixchal Gonzalez takes yearly expeditions to the Bering Sea (Northern Pacific Ocean) where she takes measurements of phytoplankton 11

Figure 2. Phytoplankton population change with varying temperature and constant salinity. 13