Wikijunior:The Book of Estimation/Introduction

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Wikijunior:The Book of Estimation
Introduction Numbers

Take a look at this news report (at http://en.wikinews.org/wiki/Bird_flu_may_infect_20_percent_of_world's_population,_kill_millions ). The Spanish 'flu killed 50 million people. But is that exact? Surely it could have killed 50,000,000,001? Or perhaps 49,999,999,999? Of course! The numbers are not exact because it is approximate. But what do exact, approximate, and estimate mean in mathematics? How can we estimate?

What is estimation?[edit]

Definition table

  • Approximation: Making numbers simpler
    • Approximate: (adj) A number that is close to the exact value
  • Estimation: Guessing data, but trying to be close enough
    • Estimate: (v) To guess data while trying to be close enough
  • Exact value: The 100% correct value of a number

Take a look at this number.

213,487,104,577

Big number, huh? Now let's make it a tad simpler.

213,400,000,000

Ta-daa! It's much neater than the previous one. So what did we do? Did we use...

  • ...estimation?
  • ...approximation?

The answer is approximation. Approximation is the science of making numbers simpler. However, approximation is a crucial element of estimation. In a broad sense, estimation means guessing some kind of value and trying to be as close to the real value as we want. Sometimes the result can be really far off, however, as we will see later.

There are different ways of estimating. In mathematics, we often estimate the result of an operation because we don't want to waste time calculating the whole thing. We do the same in daily life. Sometimes, different methods of estimation may be suitable in some contexts, but unsuitable in others. We shall explore that further on in this book.

An error occurs when there is a difference between the exact and approximate value of something. We will discuss this in detail later as we need to know about some other basic concepts of approximation and estimation first.

Why estimate?[edit]

Why should we estimate? First, estimation can give us the rough idea about something. Sometimes, we need to calculate something but do not have a calculator or paper and pen. We must use mental mathematics to get the answer. That' where estimation comes in handy. Secondly, estimation can allow us to see whether our answer is reasonable. Consider the following example.

34+62=299

By estimating the answer of 34+62=299, we find that the answer is unreasonable and incorrect.

Why should we use approximation?

We can use approximation to remember something more easily. For example, do you think it is easier to remember that 10 million people died in the Spanish 'flu pandemioc, or that 10,794,194 people died? Probably 10 million! We can also use approximation when the exact value of something is unknown or constantly changing. The world population is one of the best examples. It is changing constantly, because people are born every second. We can never find out the exact value in measurements. This will be discussed later on.

Vocabulary list[edit]

Exercise[edit]

Give one example of estimation and one example of approximation in daily life.

Answers: Answers will vary.