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Millions, Billions, Zillions: Defending Yourself in a World of Too Many Numbers

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An essential guide to recognizing bogus numbers and misleading data

Numbers are often intimidating, confusing, and even deliberately deceptive--especially when they are really big. The media loves to report on millions, billions, and trillions, but frequently makes basic mistakes or presents such numbers in misleading ways. And misunderstanding numbers can have serious consequences, since they can deceive us in many of our most important decisions, including how to vote, what to buy, and whether to make a financial investment. In this short, accessible, enlightening, and entertaining book, leading computer scientist Brian Kernighan teaches anyone--even diehard math-phobes--how to demystify the numbers that assault us every day.

With examples drawn from a rich variety of sources, including journalism, advertising, and politics, Kernighan demonstrates how numbers can mislead and misrepresent. In chapters covering big numbers, units, dimensions, and more, he lays bare everything from deceptive graphs to speciously precise numbers. And he shows how anyone--using a few basic ideas and lots of shortcuts--can easily learn to recognize common mistakes, determine whether numbers are credible, and make their own sensible estimates when needed.

Giving you the simple tools you need to avoid being fooled by dubious numbers, Millions, Billions, Zillions is an essential survival guide for a world drowning in big--and often bad--data.

176 pages, Hardcover

Published November 6, 2018

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About the author

Brian W. Kernighan

28 books331 followers
Brian Wilson Kernighan is a computer scientist who worked at Bell Labs alongside Unix creators Ken Thompson and Dennis Ritchie and contributed greatly to Unix and its school of thought.

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Displaying 1 - 22 of 22 reviews
Profile Image for Brian Clegg.
Author 163 books3,187 followers
November 26, 2018
The news is riddled with numbers that we often taken for granted. Brian Kernighan sets out to give us the tools to test numbers in the headlines and see if they really add up. The fact that they often don't is made clear by the range of examples Kernighan gives where a news source has got a value wrong, whether it's out by a factor of a thousand, using the wrong units or impossibly accurate, perhaps due to a spot of calculator work converting one unit to another.

This isn't the first book to take on misleading numbers - as well as the classic How to Lie with Statistics, there was the excellent The Tiger that Isn't. Although Kernighan covers many of the common errors in this slim volume, I didn't get the same sense of fascination here as I did with those earlier titles (particular The Tiger). Kernighan gives us useful tips on checking numbers, but often the examples felt like hard work for numbers it's hard to care too much about (the US's 60 billion barrel oil reserve, for example (actually 60 million)) - carefully choosing your examples in a book like this is really important.

The techniques Kernighan gives, such as scaling numbers to individuals rather than the population as a whole, knowing some basic values and constants, Little's Law, the rule of 72 and approximations of powers of 2 are all great - though I confess I've already forgotten what Little's Law and the rule of 72 are and will have to go back and check. But the book didn't engage me the way that The Tiger that Isn't did (it could be partly that the The Tiger uses more British examples, but it also has a more approachable writing style).

However, books like this are essential in a world where numbers are increasingly used to bamboozle us. This is a very welcome addition to what I hope will be a growing genre.
Profile Image for Hasta Fu.
123 reviews2 followers
June 2, 2025
*Millions, Billions, Zillions: Defending Yourself in a World of Too Many Numbers* by Brian W. Kernighan is a concise, accessible guide to developing numerical literacy in an era overwhelmed by misleading data. Published in 2018 by Princeton University Press, this 176-page book aims to equip readers, even those wary of math, with tools to critically evaluate numbers encountered in daily life—whether from media, advertising, or politics.

Kernighan, a renowned computer scientist and professor at Princeton, uses a friendly, conversational tone to break down complex numerical concepts. The book covers topics like understanding large numbers, units, dimensions, and spotting deceptive graphs or overly precise figures. Through real-world examples, such as misleading journalism or questionable statistics, he illustrates how numbers can be manipulated to confuse or deceive. Reviewers praise its simplicity, requiring only basic arithmetic knowledge, making it ideal for a broad audience, including self-proclaimed “math-phobes.”

Probably I was too distracted with a lot of borrowed books in my library so I skipped from one book to another most of the time. But this also means that this book has not succeeded to catch my prolonged attention. When I found a misprinted number in news website (mostly self-run media), I tend to think that it is because the people nowadays don't have the strict writing technique compared to those of the past. Kernighan pointed out that old media also make same mistake.

One story about strange number published because of the imperial and metric system conversion, shows that precision is not the top method to go for everytime. Human tend to remember round numbers instead of 133, 2424, etc. But filling an airplane with 5000 liters of aviation fuel instead of 5000 gallons did cause a disaster.

Critics highlight its practical approach, offering shortcuts to assess data credibility and make reasonable estimates—skills vital for informed decision-making in areas like voting or financial investments. For instance, a ZME Science review notes Kernighan’s example of questioning a claim about 20 billion barrels of oil for plastic bottles, encouraging readers to use common sense to spot errors. Ben Rothke at RSA Conference emphasizes its relevance in information security, where dubious statistics, like data breach costs, are rampant, calling it a “lighter, entertaining” complement to more technical works.

However, some critiques exist. The Mathematical Association of America points out that parts may feel like common sense to mathematically inclined readers, and the lack of an index is a noted flaw. The writing, while clear, can occasionally feel dry due to repetitive examples of media errors. Still, reviewers like Jacqueline Cutler at NJ.com commend Kernighan’s approachable style, likening him to a “mellow friend” rather than an aloof academic.

Overall, the book is recommended as an “interesting supplement” for navigating a data-saturated world. It’s praised for fostering skepticism and empowering readers to avoid “number abuse”. Never believe a number because it is a number.
Profile Image for Ben Rothke.
364 reviews53 followers
December 17, 2018
The world of information security is awash in figures and statistics. From the estimated expensive costs of password resets, to cost of a data breach studies, the endlessly quoted Verizon Data Breach Investigation Report, to the near monthly hundreds of millions of customer’s data breaches, and countless more.

For anyone who wants to understand how to effectively use data in the world of information security, the definitive guide is Measuring and Managing Information Risk: A FAIR Approach, by Dr. Jack Freund and Jack Jones. For those that want to understand how the media often misuses numbers and statistics, a much lighter and more entertaining read is Millions, Billions, Zillions Defending Yourself in a World of Too Many Numbers, by noted computer scientist Brian Kernighan.

In this short and enjoyable reference, Kernighan shows how the media often uses numbers, graphs, figures and more; but far too often either misreports them, or uses them in misleading ways. There are many reasons for this, including rushed deadlines, their inherent misunderstanding of how to use statistics, not understanding the underlying issue and much more.

Kernighan gives many examples where billions and trillions are swapped. He also provides many examples of where conversions to/from metric values are done incorrectly, where orders of magnitude errors are erroneously reported.

The bigger issue is not simply that the wrong figure is used by reporters, rather people and businesses act on them, and policy decisions are based on them. Once implemented, they are often hard to correct.

In the book, Kernighan give many examples and provides ways to detect being fooled by suspect figures. The often inability of popular media to effectively use numbers and statistics, combined with the rise of fake news, makes it an imperative for readers to be skeptical when these numbers are being reported.

Be it from the media, politicians or clueless neighbours, numbers and statistics are often used to confuse us. This in turns makes it important for readers not to take these figures at face value. By be numerically illiterate, a person runs the risk of being manipulated.

Numbers, graphs and statistics can often be misleading and misrepresented. In Millions, Billions, Zillions Defending Yourself in a World of Too Many Numbers, Kernighan
Profile Image for Behrooz Parhami.
Author 10 books35 followers
December 19, 2023
Brian Kernighan [1942-], a Canadian computer scientist, was one of the three scientists at Bell Labs who revolutionized their field by devising the UNIX operating system. Later, he co-authored the first book on the highly-influential C programming language. So, this book on huge numbers and their impact on our society, hailed by the publisher as "an essential guide to recognizing bogus numbers and misleading data," should be considered a side project for Kernighan.

We humans have the ability to recognize small numbers built into our brain by evolution. We immediately recognize the difference between one predator and three predators following us. Larger numbers are abstract constructs whose recognition depends on our acquired computational abilities. In modern times, we have developed an appreciation for million and billion, in part because of the widespread use of the terms "millionaire" and "billionaire." Even here, most people have no idea how long it takes to count from 1 to 1,000,000. Trillion-dollar national budgets are beyond the grasp of even the most-numerate people.

With the help of examples drawn from journalism, advertising, politics, and other domains, Kernighan shows us how numbers can mislead and misrepresent. Consequences of misunderstanding numbers can be serious in domains such as voting, purchasing, and making investment decisions.

One essential skill for our modern world is the ability to tell whether a number is a ballpark estimate or the result of precise calculations. Another is the skill to quickly determine whether a number makes sense. Ballpark estimates are misrepresented if they come with too many digits of precision. A columnist's 1996 claim that Americans receive 2 million tons of junk mail per day is easily refuted by dividing the number by the US population and then estimating the load of a mail-carrier for a residential neighborhood. Complementing the ability to recognize fake or misleading numbers is learning how to make our own estimates when needed.

Collectively, the skills mentioned in the preceding paragraph, which this book attempts to develop, help us avoid becoming a victim of inadvertent or deliberate number abuse.
61 reviews5 followers
November 16, 2018
The book equips the skeptic's toolset with some practical quick math and estimation skills. The author draws on examples from the press, social media, and his own encounters out in the wild. Written in a conversational tone, the book is a really quick read.

Most of the examples are either from 2007-2008 or 2017, which makes it look a bit like the decade in between was a golden age of accuracy. Nevertheless, the examples show that whether intentionally or not, information out there can be at the very least inaccurate, if not entirely misleading.

Self-defense is a great concept in this context, especially in the age of "fake news" and information being shared on social media.

I would have liked to see exercises at the end of each chapter like the Fermi problems in Chapter 13.
79 reviews7 followers
August 9, 2020
Good straightforward introduction to rough estimation as a defence against wrong or misleading figures. Not wildly exciting -- it's largely a catalogue of quantitative errors in the media, together with explanations of how an attentive reader could have noticed the numbers were off and made a decent guess at why and by how much -- and if you've thought about this sort of thing before then it might not teach you anything. But it's an easy read, written simply but not patronisingly, and I appreciate that it wasn't padded out to 300 pages. Could be great for a teenager with an interest in critical thinking and spotting errors in supposedly authoritative places.
341 reviews3 followers
February 4, 2019
This is a great book to read with a math class, kids who have passed 5th grade arithmetic. There are a few rules of thumb which these students are not ready to fully understand the origin of (half time and compound interest), and these can be safely skipped; everything else is accessible. I intend to read it with my 5th and 6th graders, and assign to them to look through magazines and articles for calculations, stark headlines and shouting graphs which demonstrate the points made in the book, as well their genuine informative counterparts.
Profile Image for Urey Patrick.
346 reviews19 followers
March 27, 2019
Interesting... fun... useful and educative. Joins a hand full of similar books explaining and illustrating how to discern factual realities in the blizzards of misleading, mistaken or otherwise incorrect mathematical news items and claims that besiege us daily ... greatest, least, most, startling percentage changes, graphical anomolies, etc. Well worth reading - as are earlier books in the genre such as Innumeracy by John Allen Paulos, How to Lie With Statistics by Darrel Huff, Damned Lies and Statistics by Joel Best... etc.
84 reviews2 followers
November 21, 2024
數據會說話,還是會騙人?

我對數字非常敏感,很多時候都能指出當中的錯誤或識破操弄數據的目��。

例如今日新聞:XX集團宣布,截至11月11日晚上11時59分,優惠期間內,購物用戶數按年增長超過20%,XX採銷直播訂單量按年大升3.8倍,有逾1.7萬個品牌成交額按年增長超過5倍⋯

這些通告幾乎毫無意義,因為沒有實質數字,尤其是沒有用過去幾年的資料作參考,就好像孩子告訴母親默書分數增長一倍,原來只是由13分變成26分:還是不合格。

《一輛運鈔車能裝多少錢》(Millions Billions Zillions)這本書指出,「數感」(對數字的感覺)是可以訓練出來的。作者提醒讀者了解數據時要注意的地方,例如:數據提供者、來源、表達方式、目的,又如何利用簡化和速算快速查證數據的真確性,最後還建議讀者準備一份清單,記熟一些常用數字及其關係,使將來驗證數據時更容易掌握。

如果你是一名「數盲」(innumerate),本書會教你找出數據陷阱,提升你快速理解數字的能力;如果你打算面試,本書教你的技巧會讓你在理解數字方面過人一等,令人另眼相看;如果你「數感」過人,本書更會令你如虎添翼!推薦閱讀。
117 reviews
July 12, 2020
A lovely, short, readable book that equips the reader with a handful of tools to think critically about the numbers we read in the media. It’s breezily written in a friendly tone and is filled with engaging examples. Thoroughly recommend it - and I say this as someone whose mental arithmetic is pretty poor.
Profile Image for Turquoise.
172 reviews3 followers
June 22, 2020
A fun read with lots of interesting examples of how media reporting can go wrong when people are not careful about numbers. The book offers some helpful tips and tricks for estimating values yourself based on partial information. This could work well in various classroom settings.
Profile Image for Marcus.
21 reviews2 followers
November 20, 2020
A straightforward overview of the critical thinking skills needed to navigate the numbers of everyday life. Clearly written and surprisingly charming. However, it has little to offer anyone who already tries be critical about the numbers they face.
Profile Image for Duane Gosser.
363 reviews1 follower
May 4, 2021
A fun read...if you like to pay attention/question the data that floods our TV/radio/phones every day.
Demonstrates how easy it is to verify/validate the BS/sloppiness factor quickly and easily.

I would recommend especially in current climate.
Profile Image for Sean.
37 reviews6 followers
November 5, 2021
I picked up this book based on a recommendation as well as the author.

It was a great, short book with tons of wonderful examples of using simple arithmetic and estimation in not only thinking about the data you encounter in public discourse but in other parts of your life as well.
5 reviews1 follower
January 1, 2026
In twenty years when all my friends' kids are graduating high school you'll find Aunt Esther annoying them by eschewing a cash graduation gift in favor of this little toolkit for defense against the news numbers arts
Profile Image for Sara Rocutto.
512 reviews9 followers
October 10, 2019
Ho letto la versione italiana recentemente pubblicata da Egea. Utile, piacevole, semplice e curioso, anche per chi ha studiato ingegneria ;)
Profile Image for Dixie.
Author 2 books20 followers
October 16, 2019
Interesting and useful, even to someone like me who struggles with math.
Profile Image for Tim.
91 reviews
March 19, 2021
Short and easy reading with interesting examples of numbers and how they are used/misused.
Profile Image for Steve.
1,204 reviews89 followers
November 1, 2025
Fun short book about being skeptical about statistics, charts, graphs, doing back-of-envelope estimates, seeing where numbers are clearly wrong.
Profile Image for Maurizio Codogno.
Author 75 books147 followers
September 4, 2020
Spannometria presentata da un mito

[nota: esiste anche la traduzione italiana, Milioni, miliardi, fantastiliardi, che però non ho letto]. Un qualunque informatico della mia età o anche un po' più giovane, se sente parlare di Kernighan, pensa immediatamente al linguaggio C e al Kernighan-Ritchie. I più esperti sanno anche che lui è la K del linguaggio awk. È perciò buffo scoprire che è ancora attivo e ha da poco scritto questo libro, il cui scopo specifico è insegnare alla gente come non aver paura dei numeroni che ci assediano e soprattutto accorgersi degli errori marchiani che spesso si trovano nei giornali. Ho il sospetto che collezionare questi errori e le eventuali correzioni - nella stampa americana è molto più facile che capiti rispetto che da noi - sia un suo hobby. Il libro insegna attraverso tanti esempi ad applicare la nobile arte della spannometria, e quindi è altamente meritorio; forse è un po' troppo simile a un manuale, compreso il recap alla fine di qualunque capitolo, ma non ci si può aspettare nulla di diverso, no? Fatevi comunque un favore e leggetelo!
Profile Image for Melvin R.  R.  Blann IV.
65 reviews1 follower
November 20, 2023
A solid book & an easy read about how to analyze statistical claims and figure out if they’re legitimate. The author provided several simple techniques to help assess the validity of reported statistics. He also provided tons of real life examples of the news media & activist groups reporting/promoting inaccurate statistics, including several stories from The NY Times. Don’t ever take reported statistics at face value. Scrutinize them to see if they make mathematical sense.
Displaying 1 - 22 of 22 reviews

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