Advantages of the Place Value System 2

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Non-Standard Representations

The standard manner in which &ldquo;expanded representation&rdquo; is taught in schools is that 3425 = 3000+ 400+ 20 + 5. For children this is a mechanical exercise which does not give any insight into the Place Value System. This is known as the Standard Representation, where at each &ldquo;place&rdquo; only numbers &lt;=9 can be written.

We can think of the standard representation as a restriction that a person can pay Rs 3425 only in terms of 3 Thousand Rupee notes, 4 Hundred Rupee notes, 2 Ten Rupee notes and 5 One Rupee notes. But in reality, we can pay Rs 3425 is many other combinations as shown below.

For example, Row 4 represents a situation where 34 Hundred-rupee notes, 2 Ten rupee notes and 5 One rupee notes are used to pay an amount of Three Thousand Four Hundred and Twenty Five rupees.

These are called Non-Standard representations and the table above gives a number of such representations. With the structure of the Place Value Concept, writing down of non-standard representations becomes very easy. The same string of numerals, 3425 appear in the same sequence in various &ldquo;places&rdquo;.

These representations are very useful make additions &amp; subtractions easier, as will be seen in the chapters on arithmetic operations. What we do when we &ldquo;borrow&rdquo; or &ldquo;carry&rdquo; is actually writing that number in a non-standard representation. When subtracting 38 from 45, when we borrow 1 from 4 what we are actually doing is rewriting 45 in a non-standard form 3 (tens) 15 (ones). Subtracting 8 from 15 is easy.

Other Number Bases

A clear understanding of the decimal place value system makes it easy for students to understand other number bases &amp; conversions between bases. We will see this in detail in the next chapter.

Major Disadvantage

In the place value system, the value of a number can be drastically altered by inserting an additional numeral within a number. For example, 200 can be changed to 2000 or 345 can be changed to 3045. Keeping this in mind, most financial documents, like a cheque, require that the number, though stated in numeral form, also has the word form in brackets.

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