Q1. What is the rounding convention that we use in science?

Imagine that we have a set of numbers that we need to round to the nearest integer (i.e., the nearest whole number without any digits to the right of the decimal point).

1. If the first digit to the right of the decimal point is smaller than 5, then drop all digits right of the decimal point and leave the first digit to the left of the decimal point unchanged.
2. If the first digit to the right of the decimal point is larger than 5, then drop all digits right of the decimal point and add 1 to the first digit to the left of the decimal point (i.e., round up).
3. If the first digit to the right of the decimal point is 5 and the digit to its left is an even number, then drop all digits right of the decimal point and leave the first digit to the left of the decimal point unchanged.
4. If the first digit to the right of the decimal point is 5 and the digit to its left is an odd number, then drop all digits right of the decimal point and add 1 to the first digit to the left of the decimal point (i.e., round up).

Your turn...

• Given the following numbers, round each to the nearest integer:

  11.4: _______	11.5: _______	11.6: _______
  12.4: _______	12.5: _______	12.6: _______

• Given the following set of numbers, which represent a set of measurements, find their average and round the result as seems appropriate: 13, 14, 17, 18.
  
  
• Given the following set of numbers, which represent a set of measurements, find their average and round the result as seems appropriate: 14, 15, 18, 19.
  
  

What if you had a deformed trilobite fossil that is close to 2 cm long, and a metal ruler marked in centimeters. Could you measure the length of the fossil to the nearest centimeter with precision? Could you measure the length in millimeters with precision? ...in micrometers...?

Q2. What is the meaning of "significant figures?"

Q3. How do you determine the "significant figures" for a set of measurements?

Your turn...

You are given a set of observations made by different people at different times, all expressed to the appropriate number of significant figures. The observations are 12.3, 13.482, 11, 10.53. What is the average of these numbers, expressed to the appropriate number of significant figures? (Hint: the average is only valid to the level of precision associated with the least well-known observation.)

The standard deviation of a set of values provides valuable information about the variability of numbers within the set. The 95% confidence interval is a measure of the uncertainty in a set of data (assuming that they represent repeated observations of the same phenomenon). A brief explanation of standard deviation and confidence intervals is available on a separate page.

Your turn...

What is the average and standard deviation of the following numbers in set 1: 6, 12, 15, 24, 38?

Values	Average	Standard Dev	95% Conf Int
6, 12, 15, 24, 38	__________	__________	__________

What is the average and standard deviation of the following numbers in set 2: 19, 17, 21, 18, 20?

Values	Average	Standard Dev	95% Conf Int
19, 17, 21, 18, 20	__________	__________	__________

How do the averages in sets 1 and 2 compare with one another?

How do the standard deviations in sets 1 and 2 compare with one another?

How do the 95% confidence intervals in sets 1 and 2 compare with one another?

Horace Greeley famously said "Go west, young man." West is a compass direction.

The Flat Earth

Q4. What is a compass direction?

Q5. How is a compass direction described?
Ways of describing angles (refer to Cronin's Vector Primer, p. 1-3)

• degrees, minutes, seconds
• decimal degrees
• radian measure

• azimuth
• bearing
• trend
• quadrant

Q6. How do you convert a compass direction given in the quadrant system to the equivalent compass direction in the azimuth system?

Your turn...

Convert the following compass directions from the quadrant system to the azimuth system.

N32E: _______	S14E: _______	S78W: _______	N70W: _______
N48W: _______	S63W: _______	S44E: _______	N12E: _______

Q7. How do you convert a compass direction given in the azimuth system to the equivalent compass direction in the quadrant system?

Your turn...

Convert the following compass directions from the azimuth system to the quadrant system.

14°: _______	85°: _______	114°: _______	167°: _______
205°: _______	278°: _______	312°: _______	348°: _______

Compass direction as a vector quantity

Q8. What is a vector? (refer to Cronin's Vector Primer, p. 4)

Q9. What is a unit vector?

Refresher on trigonometry

Need more information on trigonometry? Visit the GeoMaths web site (www.ucl.ac.uk/Mathematics/geomath/frontpage.html) for help with mathematics in a geological context.

Q10. What are the rules for converting azimuth to Cartesian 2D coordinates of a unit vector?

Your turn...

Apply your rules to find the Cartesian 2D coordinates of the following azimuths:

• 47°: ______
• 142°: ______
• 205°: ______
• 319°: ______

Q11. How is a compass direction measured?
(Discuss Earth's magnetic field and body forces.)

Q12. What is magnetic declination?

Q13. Why is magnetic declination important?

Q14. How do you determine the declination of a given location at a given time?
The most accurate way to find the declination of a given point on Earth is to use the declination calculator maintained by the National Geophysical Data Center (NGDC), accessible on the web at http://www.ngdc.noaa.gov/seg/geomag/jsp/Declination.jsp. Directions for using the calculator are available at http://www.ngdc.noaa.gov/seg/geomag/magfield.shtml

Your turn...

Determine the location of the Baylor Science Center using a GPS receiver*, and then use the NGDC declination calculator to determine the magnetic declination today at the BSC.

• latitude: _____________
• longitude: ____________
• declination: ____________

The URL of this page is www3.baylor.edu/~Vince_Cronin/IntroStructGeol/StructLabBk1.html
Modified August 22, 2006

All original content in these web pages is copyright (© 2006) by Vince Cronin, and may be used with attribution for non-profit educational and research purposes.