Estimation in Daily Life

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The term &ldquo;estimation&rdquo; has been used here in a sense that is slightly different from the classical sense. Here we use estimation as a &ldquo;back of the envelope&rdquo; or a &ldquo;reasonably correct&rdquo; calculation. Estimation can be called an educated guess.

Most real-life situations demand a quick estimate rather than an exact answer. For example if we hear that someone is 1.76 m tall, and we are familiar with heights in terms of feet &amp; inches, what we need immediately is an approximate answer.

Estimation and Math Proficiency

A 2013 study by Joonkoo Park and psychologist Elizabeth Brannon, both then at Duke University, found that students could improve their math proficiency through training that engaged their ability to estimate quantities.

Possibly training in estimation also strengthens number sense, which in turn strengthens math proficiency.

Rounding Numbers

Rounding of numbers is the first step towards estimating. We know that certain numbers in our decimal place value system make calculations easier. They are multiples of powers of ten and numbers ending with 5. So, given an expression for estimating, we round the numbers involved in the calculation to the nearest 5s, 10s or 100s.

If the numbers involved in the above operations have decimals, then we will first have to round them to a nearest number which will make the computation easier. For example rounding 1.78 to 1.5 or 2 will make the computations easier. The decision on which rounded value to take would depend on – the ease of computation and the accuracy of the estimation required.

Rounding is a mechanical process. Hence computer software have formulas for rounding off.

Estimation depends of the context in which it is requires. Hence it cannot be mechanized.

These estimate procedures are simple enough to be done mentally. Let us see some examples.

Four Basic Arithmetic Operations
 * 1) The four basic arithmetic operations
 * 2) Square roots and Cube roots
 * 3) Conversions of Weight, Length, Area &amp; Volume

Multiplication &amp; additions of powers of ten is easy. Hence one strategy is to round the numbers to the nearest powers of ten.

For example, 48 X 52 is approximately 50 X 50 which is 2500.

Square Root 

We use the idea that square root of 100 is 10 and that of 10,000 is 100 and so on. So separate the number into 2s, starting from the right. Find the approximate square root of the left most set and add a 0 for every set of 2 numbers.

Square root of 48,567. Write the number as 4 85  67. Square root of 4 is 2. So the answer is roughly 2 0 0. Ie 200.

Squares and square roots show the following relational patterns, which will help us in estimating..

Cube Root

Use a technique similar to that for square roots, except that now group the numerals into sets of 3 starting from the right.

Cube root of 48, 567. Write the number as 48 567. Cube of 3 is 27 and that of 4 is 64. 48 is somewhere between and so let us take the cube root as 3.5. Replace 567 by a 0. Hence the cube root would be around 35.

Patterns of products of numbers

If product of 2 numbers ends with a particular number then we can make guesses as to the ending numbers of the 2 numbers which were multiplied.

Converting Kgs to Pounds

The multiplying factor is approximately 2.2. Mentally it can be done by doubling a number and adding one tenth of the result.

3 kgs = 3 X 2 -&gt;6 -&gt; 6 + 0.6 = 6.6

Converting Inches to cms

The multiplying factor is approximately 2.5. Mentally it can be done by doubling a number and adding half of the number to it..

3 inches = 3 X 2 -&gt; 6 + 1.5 = 7.5

Converting miles to Kms

The multiplying factor is 1.6. Mentally it can be done by using 16 tables. Those who do not remember 16 tables, can add 0.6 of a number to the number. 0.6 is got by multiplying by 6 and taken a tenth of it.

5 miles = 5 + 5X6/10 = 5 + 3 = 8

Using approximate value of &pi;

Depending on the context we can use or 3.14 or  or even just 3!

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