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 (http://bearspace.baylor.edu/Vince_Cronin/www/StructGeol/StdDevNotes.pdf).

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?

The URL of this page is bearspace.baylor.edu/Vince_Cronin/www/StructGeol/StructLabBk1A.html
Modified November 6, 2008

All original content in these web pages is copyright (© 2006-2008) by Vince Cronin, and may be used with attribution for non-profit educational and research purposes.