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OCEAN LAB 01 Laboratory Skill Review
Scientific Measurements and the Metric System Objectives
- To understand how to make measurements utilizing various instruments
- To learn how to use the metric system
- To convert between the metric system and the English (American) System of length, volume, mass and temperature for measurements
- To apply metric measurements in future laboratories
- To express calculations and measurements to an appropriate level significance
These exercises cover math and map skills that you will be using in future labs. Since these skills often cause big time issues in future labs, because of varied skill levels, we use the first lab of the semester to get everyone up to speed. If you are already strong in these areas, you should finish today’s lab quickly. If, however, you are weaker, you may need more time. Show ALL work. (You may use a calculator.)
Inequalities 6 > 2 means 6 is greater than 2. 4 < 10 means that 4 is less than 10. 2 < X < 4 means X is a number greater than 2 and less than 4.
(The alligator mouth opens towards the larger meal!)
1. Insert correct symbol10 ____ 100 / 2. Insert correct symbol:
100 ____ 1
3. Use symbols and variable X to describe a number between 6 and 18. / 4. Use symbols and variable X to describe a number that is less than 2.5.
Scientific notation
Scientific notation is a simpler way of writing long numbers. Scientific Notation requires that the final number be between 1 and 10. For example, 23 x 10-4is not in scientific notation. (Solve these without a calculator!)
45600 = 4.56 x 104 / For numbers ≥ 10, move the decimal to the left and the exponent is +.0.000678 = 6.78 x 10-4 / For numbers < 1, move the decimal to the right and the exponent is –.
5. Write in scientific notation:
0.0000237 / 6. Write in scientific notation:
120,400
7. Write out (expanded):
2.5 x 10-6 / 8. Write out (expanded):
3.9 x 104
Introduction
For scientists to communicate their results to other scientists around the world, there must be some uniformity in units of which their data are expressed. In this week’s lab, you will practice making precise quantitative measurements; you will learn to interpret and to convert those measurements in a uniform way; and you will learn to express the precision of your measurement.
A. MEASUREMENT PRECISION AND SIGNIFICANT FIGURES
In science it is important to be honest when reporting values. A measurement cannot be more precise than the equipment used to make the measurement. In making a calculation, we must report the final value with no more precision than the least precise value used in the calculation. We achieve this by controlling the number of significant figures used to report the measurement. The number of significant figures in a measurement, such as 9.15647, is equal to the number of digits that are confidently known (9,1,5,6,4 in this example) plus the last digit (7 in this example), which is an estimate or approximation. As we improve the sensitivity of the equipment used to make a measurement, the number of significant figures increases.
For example, you might use a bathroom scale, a postal scale and one of the lab balances to weigh a small package. Each of these devices has a different level of precision. A table of possible values is shown in Table 1.
Table 1. Mass of a small package using three different measurement methods
Measurement Device / Mass (kg) / Precision / Significant FiguresBathroom scale / 2 kg / ± 1 kg / 1
Postal Scale / 2.10 kg / ± 0.01 kg / 3
Lab Balance / 2.108 kg / ± 0.001 kg / 4
In our example in Table One, each of the masses is reported to the correct number of significant figures based upon the precision of the device.
Here are some rules for counting significant figures:
Zeros within a number are always significant.
• In Table One, 2.108 has four significant figures.
• The number 4,005 has four significant figures.
Zeros that do nothing but set the decimal point are not significant.
• The number 4,000 has one significant figure.
• The number 23,000,000 has two significant figures.
Zeros to the right of the decimal point are significant.
• The number 213.00 has five significant figures.
• In Table One, the number 2.10 has three significant figures
Mathematical Operations and Significant Figures
When combining measurements having different degrees of precision, the precision of the final answer can be no greater than the least precise measurement. Thus, when measurements are added or subtracted the result can have no more decimal places than the least precise measurement. When measurements are multiplied or divided, the result can have no more significant figures than the least precise measurement.
For example, suppose you were to use your calculator to add the weights of several components of a sea water sample, as shown in Table 2.
Table 2
Component / Weight (g) / CommentsNaCl (salt) / 29.82 / 2 decimal places
MgSO4 (magnesium sulfate) / 4.0103 / 4 decimal places
H2O (water) / 1000.0 / 1 decimal place
Total Weight (incorrect answer) / 1033.8303 / As seen on calculator
Total Weight (correct answer) / 1033.8 / 1 decimal place
The total weight of 1033.8303 g has four decimal places, but one of the measurements has only one decimal place (the water). So the correct answer to this problem is 1033.8 g.
Here’s an example using division. If a boat travels 100.12 nautical miles (nm) in 2 hours, what is the average speed over that time? The speed of the boat is
100.12 nm / 2 hours = 50.60 nm/h
However, since 2 hours only has one significant figure, the correct answer is
51 nm/h
9. Round 3.6258 to two decimal places precision / 10. Round 5.56 to the ones place precision11. 12.7 cm + 6.43689 cm = / 12. 12.7 cm – 3 cm =
13. 1270 cm + 1 cm = / 14. 30 cm – 7 cm =
15. 12.7 cm x 8.43689 = / 16. 12.7 cm ÷ 3 =
B. THE METRIC SYSTEM
The metric system (International System or SI) is used worldwide, with the exception of the United States. This system is very easy to understand and use. There are three basic metric measurements upon which the system is based, length, volume and mass. The specific base units of measure are: the meter (m) for length, the liter (L) for volume and the gram (g) for mass. To these base units, prefixes can be added to express smaller or larger units. Since the metric system is based on powers of ten, these prefixes reflect changes that are in multiples of ten. This makes converting within the metric system quite easy by simply moving the decimal point.
Prefix Power Decimal Fraction of 10
kilo (K) 103 1,000 one thousand
hecta (H) 102 100 one hundred
deca (D) 101 10 ten
BASE UNIT 100 1 one
deci (d) 10-1 0.1 one tenth
centi (c) 10-2 0.01 one hundredth
milli (m) 1 10-3 0.001 one thousandth
micro (μ) 10-6 0.000001 one millionth
nano (ç) 10-9 0.000000001 one billionth
Unit conversion
When converting units, multiply your original number by a fraction that equals 1. (Remember, you can multiply any number by 1 without changing its meaning.) The fraction is a conversion factor with the units you want to cancel out on the bottom and the units you want to end with on the top. For example, to convert centimeters to inches, you multiply by the fraction that shows that 2.54 cm = 1 inch. It doesn’t matter which number goes on top, because they are equal, so put the number on top with the unit you want at the end, and the unit on bottom you want to cancel out.
To convert 3605 cm to inches:
X in = 1 in
3605 cm 2.54 cm Now we cross-multiply to solve.
X in = (1 in)(3605 cm) = 1419 in
(2.54 cm)
Notice that centimeters cancel on the right, and you’re left with inches.
1 mi = 5280 ft 1 in = 2.54 cm1 ft = 12 in 1 km = 0.6214 mi / 1 km = 1000 m
1 m = 100 cm / 1 g = 0.035 oz
1 kg = 2.205 lbs / 1 cm/yr = 10 km/my
1 km/hr = 0.2778 m/s
17. Convert 34.2 km to miles. (Show ALL work, with units – like one of the examples above)
18. Convert 6310 ft to miles.
19. Convert 32.6 cm/yr to km/yr.
20. Convert 2 g to kg.
21. Convert 25 L to mL
22. Convert 0.5 μm to cm
22. Convert 544 m to mm
23. Convert 4 mg = ______g = ______kg
24. Convert 168 km = ______m = ______cm = ______mm = ______μm
Speed
Like highway speed, 70 miles/hr, speed = distance ÷ time.
Solved, algebraically, for distance and time, you get three total equations:
Speed (S) = Distance (D)/Time (T)
S = D/T
To solve for DISTANCE (D),
multiply both sides by T
T x S = (D /T)x T
D = SxT
To solve for TIME (T),
divide both sides by S
D/S = (SxT)/S
T = D/S
A. If it takes 3.2 hours to arrive at a party, and you travel at 43 miles per hour, how far do you travel?
D = SxT D= 43 mi/hr x 3.2 hr D = 137.6 miles D = 140miles
End members for precision are 43.4 miles and 42.5 miles and 3.15 hours and 3.24 hours. End member distances: 3.24 hr x 43.4 miles/hr = 140.6 miles; 3.15 hr x 42.5 miles/hr = 133.9 miles; the hundreds place is the same for all; the first place (from left) to change is the tens place, so round original answer to tens place.
B. If you travel 6 miles by bicycle at an average of 11 miles per hour, how long does it take you arrive?
T = D/S
T = 6 mi/11 mi/hr T = 6 mi x 1 hr/11 mi T = 0.5455 hr T = 0.5 hr
End members for precision are 6.4 miles and 5.5 miles and 11.4 mph and 10.5 mph.. End member times: 6.4 mi ÷10. 5 miles/hr = 0.61 hr; 5.5 mi
÷ 11.4 miles/hr = 0.48 hr; there are no places the same for all; the first place that changes is one decimal place, so round to one decimal place.
C. If you walked 3 miles, and it took you 1.4 hours to do so, how fast did you walk?
S = D/T
S = 3 mi/1.4 hr S = 2.143 mi/hr S = 2 mi/hr
End members for precision are 3.4 mi and 2.5 mi and 1.45 hr and 1.35 hr. Thus, end member distances: 3.4 mi ÷1.35 hr = 2.5 mph; 2.5 mi ÷ 1.45 hr = 1.7 mph; there are no places the same for all; the first place that changes is the ones place, so round original answer to the ones place.
Remember to round for correct precision in answer. Show ALL work – all steps – with units throughout!
25. If a tsunami travels through the water frompoint A to point B (1602 km apart) in 2.1 hrs,
how fast was it moving in km/hr?
(Ranges: 1602.4 km, 1601.5 km; 2.14 hr, 2.05 hr)
26. If a wave travels at a speed of 4.5 km/hr.
How far can it travel in 3.3 hours?
(Ranges: 4.54-4.45 km/hr; 3.34-3.25 hr)
27. If longshore currents travel at a speed of 3.1
km/hr. How long, in hours, would it take it
to travel 6 km?
(Ranges: 3.14-3.05 km/hr; 6.4-5.5 km))
/ 28. Numbers to the right of each volcanic landform indicate age of each island in millions of years (m.y.) and distance away from next youngest landform.
Example: the third volcano from the bottom right corner is 12 million years old and 100 km away from the center of the 8 million year- old volcano. If you are using a hotspot track to determine the speed that a plate has been moving over the hotspot, measure the distance between islands and then determine the amount of time it took the plate to move that distance. For this exercise, calculate the average speed the plate traveled BETWEEN each island.
Remember: 1 cm/yr = 10 km/my
**Complete this entire exercise by
keeping precision
Age range
(m.y.) / Distance between
islands (km) / Average rate of plate motion during interval (km/m.y.) / Average rate of plate motion during interval (cm/year)
0-8 / 270
8-12 / 100
12-30 / 450
30-36 / 480 / 480 km/6 my = 80 km/ my / 8.0 cm/yr
36-41 / 400
41-43 / 160
43-45 / 160
45-54 / 1080
54-62 / 960
62-67 / 600
67-93 / 390
93-114 / 315
114-132 / 270
Precise to ones place / Precise to one decimal place
29. The currents around the Hawaiian Islands flow at about 4.0 cm/second. Assume your hat blew off just at Haunama Bay. How long (in hours) before you could pick it up in Waikiki by the Natatorium? (Hint: The distance is about 9 miles; 1 mile = 1.61 km)
30. Show your workTable 3. Metric and English (American) Conversion Factors
Length / Volume (Liquids):1 cm = 0.394 inches (in) / 1 ounce (oz) = 29.6 mL 1 L = 10 dl
1 m = 39.4 inches / 1 quart (qt) = 0.946 L 1 L = 1000 mL
1 km = 0.621 miles / 1 gallon (gal) = 3.785 L 1 mL = 1000 μl
1 in = 2.54 cm / 1 pint (pt) = 16 fluid oz
1 yard = 0.914 m / 1 qt = 2 pt
1 mile = 1.61 km / 1 gal = 4 qt
1 mile = 5280 ft / Mass:
1 foot = 12 in / 1 g = 0.0353 oz
Area: / 1 kg = 38.28 oz (2.2 lbs)
1 sq. cm (cm2) = 0.155 in2 / 1 metric ton = 1000 kg
1 m2= 1.2 yd2 / 1 pound (lb) = 454 g
1 km2= 0.386 mile2 / 1 lb = 16 oz
1 ft2= 929 cm2 / 1 oz = 28.35 g
1 mile2= 2.59 km2 / Volume (Solids):
Temperature: / 1 cubic foot (ft3) = 28,320 cm3
°F = (9/5 °C) + 32 / 1 yd3 = 0.7646 m3
°C = 5/9 (°F – 32)
C. TEMPERATURE MEASUREMENTS
Most of you are familiar with the Fahrenheit scale for temperature measurement. In science, the Celsius (or centigrade) and Kelvin scales are used. Scientific temperature readings in biology are often measured in degrees Celsius as opposed to Kelvin. Countries other than the United States also use the Celsius scale for temperature measurement. Conversions between the Celsius and Fahrenheit scales are done with the following formulas:
°F = (9/5 °C) + 32 or °C = 5/9 (°F – 32)
For example, to convert 22°C to °F, use the first formula:
°F = (9/5 °C) + 32
= (9/5 x 22) + 32
= 39.6 + 32
= 72 °F
31. Corals grow between 18 to 32 °C. Convert this range to °F.32. The sea surface temperature for Oahu on June 28, 2008 is 81.1°F. Convert this range to °C.
DIRECTION
Compass Rose
Compass points
# / Compass point / Abbr. / True heading / # / Compass point / Abbr. / True heading1 / North / N / 0.00° / 11 / East-southeast / ESE / 112.50°
2 / North by east / NbE / 11.25° / 12 / Southeast by east / SEbE / 123.75°
3 / North-northeast / NNE / 22.50° / 13 / Southeast / SE / 135.00°
4 / Northeast by north / NEbN / 33.75° / 14 / Southeast by south / SEbS / 146.25°
5 / Northeast / NE / 45.00° / 15 / South-southeast / SSE / 157.50°
6 / Northeast by east / NEbE / 56.25° / 16 / South by east / SbE / 168.75°
7 / East-northeast / ENE / 67.50° / 17 / South / S / 180.00°
8 / East by north / EbN / 78.75° / 18 / South by west / SbW / 191.25°
9 / East / E / 90.00° / 19 / South-southwest / SSW / 202.50°
10 / East by south / EbS / 101.25° / 20 / Southwest by south / SWbS / 213.75°
21 / Southwest / SW / 225.00° / 27 / West-northwest / WNW / 292.50°
22 / Southwest by west / SWbW / 236.25° / 28 / Northwest by west / NWbW / 303.75°
23 / West-southwest / WSW / 247.50° / 29 / Northwest / NW / 315.00°
24 / West by south / WbS / 258.75° / 30 / Northwest by north / NWbN / 326.25°
25 / West / W / 270.00° / 31 / North-northwest / NNW / 337.50°
26 / West by north / WbN / 281.25° / 32 / North by west / NbW / 348.75°
Angles
Use a protractor to measure the following angles. To ensure you’re using the protractor correctly, first ask yourself, where 0° is in your diagram. Line the protractor up so the 0 value on the protractor points at 0° on your diagram. The T in the center of your protractor should line up with your angle or line.
33. A circle encompasses 360° of arc. Starting with 0° at the top (OR NORTH) of the circle, and moving clockwise, indicate the degrees of arc encompassed by each of the four divisions indicated in the graphic.
Notice that you need to measure only one angle above to find values of all the others. / 34. What is the value of each:
a. A:______
b. B:______
c. X:______
d. Y:______
Adding and subtracting angles
1 degree (1°) can be broken into 60 equal pieces, each called 1 minute (1’); each minute is further divided into 60 equal pieces, each called 1 second (1”). Show ALL work.
35. 32°45’36” + 3°25’52” = / 36. 32°45’36” – 3°25’52” =37.
3 ¼ ° = ______° ______’ ______” / 38.
45.825° = ______° ______’ ______”
Orientation
39. Label each of the four markers as north, south, east, west appropriately./ 40. Oceanographers measure orientation of a line by how many degrees of arc it represents on a circle
(measured clockwise from North = 0°, like you did above). What is the orientation of these lines, according to oceanographers?