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10 Easy Ways to Avoid Math Mistakes

PRINCIPLES OF HYDROGEOLOGY
ESCI 337

Hints for Solving Quantitative Problems                                             

Solving numerical problems is a critical aspect of scientific work.  Your calculations must be neat and carefully done, and must be accompanied by explanations of the computations.  Here's how to do well on solving numerical problems:

Understand the Problem.

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Start with plenty of clean paper.
w Write a statement of the problem--what the situation is and what you need to find.
w Write what is "Given" information.
w Draw a picture of the situation, if applicable.


Solve the Problem.

w Break the problem into a series of smaller problems.

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Solve each smaller problem first, and then the larger one, in a logical sequence of steps that take you from what you know to what you want to know.
w    At the beginning of each step, write in words what process that step involves.
w Write the units of measurement at every step in the solution.  This really is important!
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Convert units as necessary.  For more on units, see p. 19-20 in Fetter's Applied Hydrogeology textbook.


Check your answer.

w Check to be sure your answer is reasonable.  Picture the result, if you can. 
w Check to be sure you included units of measurement in every step. 
w Check to be sure the answer is expressed in a convenient unit and order of magnitude.

w Check the number of significant figures (digits) in the answer.  For more on significant figures, see p. 18-19 in the Fetter textbook.


Get your work ready to show to another person.


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Copy your solution onto a clean sheet of paper.
w Start each problem on a new sheet of paper.
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Write no unexplained numbers or words on the paper--every mark on the page must be easily understood by the reader.
w Make it easy to read: leave lots of blank space, and put a box around the final answer.


Use the best format for clarity.

w Some solutions are best expressed with a graph.  On every graph, label each axis, including units of measurement; give title and date; and write chapter and problem number.

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Some answers are best given in tables. If your answer includes a table, make it neat.  Each column needs a heading; each heading must include units of measurement.  If applicable, show a sample calculation after the table.

w Write your name on every page.

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Staple or clip pages together, and trim ragged edges.

 


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© 2011 Laura L. Sanders.  Last updated January 13, 2011.