# CHAPTERS BY WACEK KIJEWSKI

# # Chapter 10 Estimation

We are surrounded by numbers. We count, measure, calculate, compute, estimate... Numbers quantify information; there are essential to understand facts events, processes, laws... Once information is quantified, they can carry specific meaning. They are becoming interesting or puzzling or shocking. We should develop a habit to use numbers in our judgment or assessment to verify information quickly and efficiently.

In the last chapter, we stressed how important it could be to assess result of our measurement and to present the final result with a smallest uncertainty possible. Very often, however, we do not need such a degree of accuracy or such a degree of accuracy is not possible to obtain on the basis of the data available. Still, an estimation of a quantity, often known as “order of magnitude” calculations, may be sufficient to verify the correctness of our reasoning or observation.

A student, while learning to present measured or computed numerical values of quantities in SI units, often does not “feel” whether, for example, an order of magnitude of 10^{-2 }with a unit of m^{3 }is correct for a volume of an eraser he uses, whether an order of magnitude of 10¹ with a unit of kg is correct to express mass of air in a physics laboratory, whether in order to replace four tiles (10 cm × 20 cm) in his bathroom, he should order 0.8 m² of the tiles, whether a mass of cement ordered for a passage from a street to his house is not 10 times too high, whether it could be true that a spy in a film escapes with a 100 million dollars' worth of gold in a suitcase etc., etc.

A quick rough estimation of the result could verify our calculations and provide us with useful information.

Try to improve your skill in mathematical calculation by employing different techniques by analyzing the worked examples that follow and then answer the questions in Test 7 and Test 8.

Consider the numbers that we are confronted with every day: the number of people affected by the HIV virus, the population of India, the USA deficit, the billions spent on stealth bomber, the value of German exports, the size of the Milky Way, the number of stars in the largest galaxy, the number of chess plays programmed in the Deep Blue computer while playing against Kasparov, the number of genes in our body, the number on neutrinos in our universe etc. But can we imagine what such big numbers mean? Most of us cannot. Our understanding and feeling of big numbers have not developed yet.

#### DID YOU KNOW ???? **HOW HEAVY IS A SIN?**

A preacher was giving a lecture on sins in life. He raised a glass of water and asked the audience, “How heavy do you think this glass of water is?” The students’ answers ranged from 20 g to 500 g. He then replied: “It does not matter on the absolute weight. It depends on how long you hold it. If I hold it for a minute, it is OK. If I hold it for an hour, I will have an ache in my right arm. If I hold it for a day, you will have to call an ambulance. It is exactly the same weight, but the longer I hold it, the heavier it becomes.”

If we carry our sins all the time, sooner or later, we will not be able to carry on, the burden becoming increasingly heavier. The only solution is to break with all sins: no matter how light they may be. on, the burden becoming increasingly heavier. The only solution is to break with all sins: no matter how light they may be.

Do you like anecdotes, interesting and challenging problems, fun facts, puzzles, jokes related to metric system and measurement? Read them in the 2006 on-line edition of "SI Units, Conversion and Measurement Skills",186 pp.