Table Of ContentMathematics for Water and Wastewater Treatment Plant Operators Series
Basic Math Concepts
FOR WATER AND
WASTEWATER
PLANT OPERATORS
JOANNE KIRKPATRICK PRICE
Training Consultant
~ ~~r~Fr~~i~Zr~up
'e/
BocaRaton London New Yori<
CRCPressisan imprint of the
Taylor&:FrancisGroup, an lnforma business
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 1991 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and
information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and
publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission
to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any
future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic,
mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or
retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact
the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides
licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment
has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation
without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
iii
Dedication
This book is dedicated to my family:
To my husband Benton C. Price who was patient and
supportive during the two yearits took to write these texts, and
who not only had to carry extra responsibilities at home during
this time, but alsoa,s a sanitary engineer, provided frequent
technical critique and suggestions.
To our children Lisa, Derek, Kimberly, and Corinne,
who so many times had to pitinch w hile I was busy writing,
and who frequently had to wait mfoyr attention.
To my mother who has always been so encouraging and who
helped in so many ways throughout the writing process.
To my father, who passed away since the writoinfg th e first
edition, but who, I know, would have had just as instrumental
a role in these books.
To the other memberso f my family, who have had to put up
with this and many other projects, but who maintain a sense
of humor abouti t.
Thank you for your love in allowing me to do something
that was important to me.
J.K.P.
v
Contents
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i.i i. . . . .
Preface To The Second Edition . . . . . . . . . . . . . . . . . v. i.i
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
How To Use These Books . . . . . . . . . . . . . . . . x.i . . . . . . .
1. Solving Math Problems . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. Solving for the UnknownV alue................... 7
3. Fractions..................................... 27
4. Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5. Percents...................................... 103
6. Averages..................................... 117
7. Ratios and Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8. Conversions................................... 155
• "Box method"o f conversions. . . . . . . . . . . . . . . . . 161
•Cu ft to lbs conversions . . . . . . . . . . . . . . . . . . . . . 165
• Flow conversions . . . . . . . . . . . . . . . . . . . . . . . . . . 169
• Linear measurement conversions . . . . . . . . . . . . . . 173
• Area measurement conversions . . . . . . . . . . . . 177 . . .
• Volume measurement conversions. . . . . . . . . . . . . 181
• mgfL to percent conversions. . . . . . . . . . . . . . . . . . 185
• mg/L to gpg conversions . . . . . . . . . . . . . . . . . . . . 189
•Metric conversions (metric to metric). . . . . . . . . . .1 93
• Metric/English conversions . . . . . . . . . . . . . . . . . . 199
9. Linear Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
10. Area Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
11. Volume Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
12. Scales and Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
13. Powers, Roots, and Scientific Notation . . . . . . . . . . . . . 283
14. Rounding and Estimating . . . . . . . . . . . . . . . . . . . . . . . . 313
15. Dimensional Analysis........................... 327
Answer Key. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . .3 .4 .7 . . . . . . . .
Conversion Identities
vii
'
Prefa ce to the Second Edition
The first editiono f these texts was written at the conclusioofn t hree
and a half yearos f instruction at Orange Coast College, Costa Mesa,
California, for two different water and wastewater technology courses.
The fundamental philosophy that governed the writionfg t hese texts
was that those who have difficulty in math odftoe nn ot lack the ability
for mathematical calculation, they merely have not learnoerd h, ave
not been taught, the "languagoef math." The books, therefore,
represent an attempt to bridge the gap between the reasoning processes
and the languageo f math that exists for studenwts ho have difficulty
in mathematics.
In the years since the first edition, I have continued to consider ways
in which the texts could be improvIend .t his regard, I researched
several topics including how people learn (learning styles, etc.), how
the brain functionsi n storing and retrieving information, and the
fundamentals of memory systems. Manyo f the changes incorporated
in this second edition are a resouflt t his research.
Two features of this second edition aroe f particular importance:
• the skillsc heck section provided at the beginninogf every
basic math chapter
• a grouping of similar types of calculations in the
applied math texts
The skills check featuroe f the basic math text enables the student to
pinpoint the areaso f math weakness, and thereby customizes the
instruction to the needos f the individual student.
The first six chapteros f each applied math text include calculations
grouped byt ype of problem. These chapters have been included so
that students could see the common threiand a varietyo f seemingly
different calculations.
The changes incorporatedi n this second edition were field-tested
during a three-year period in which I taught a water and wastewater
mathematics course for Palomar Community College,
San Marcos, California.
Written commentso r suggestions regarding the improvemenot f any
section of these texts or workbooks will be greatly appreciated by the
author.
Joanne Kirkpatrick Price
ix
Acknowledgments
"From the original planningo f a book to its completion, the
continued encouragement and support that the author receives is
instrumental to the succesos f the book." This quote from the
acknowledgments pageo f the first editiono f these texts is even
more trueo f the second edition.
First Edition
Those who assisted during the developmeonft the first edition are:
Walter S. Johnson and Benton C. Price, who reviewed both texts for
content and made valuable suggestionfso r improvements;
Silas Bruce, with whom the author team-taught for two and a half
years, and who has a down-to-eartwh ay of presenting wastewater
concepts; Mariann Pape, SamueRl . Peterson and Robert B. Moore
of Orange Coast College, Costa Mesa, California, and Jim Catania
and Wayne Rodgerso f the California State Water Resources Control
Board, allo f whom provided much needed support during the
writing of the first edition.
The first edition was typed by Margaret Dionis, who completed the
typing task with gracaen d style. Adele B. Reesem, y mother,
proofed both books from cover to cover and Robert V. Rmeeys e,
father, drew all diagrams (by hand) shown in both books.
Second Edition
The second edition was an even greater undertaking due to many
additional calculations and becausoe f the complex layout required.
I would first like to acknowledge and thank Laurie Pilz, who did the
computer work for all three texts and the two workboHoekrs .s kill,
patience, and mosot f all perseverance has been instrumentianl
providing this new format for the texHtse. r husband, Herb Pilz,
helped in the original format design anhde assisted frequently
regarding questionso f graphics design and computer software.
Those who provided technical revieowf various portionso f the texts
include Benton C. Price, Kenneth D. Kerri, Lynn Marshall,
Wyatt Troxel and Mike Hoover. Their comments and suggestions
are appreciateda nd have improved the current edition.
Many thanks also to the staofff the Fallbrook Sanitary District,
Fallbrook, California, especially Virginia Grossman, Nancy Hector,
Joyce Shand, Mike Page, and Weldon Platt for the numerous times
questions were directed their way during the writoinfg th ese texts.
