Non-Standard Representations

We have become so familiar with the number system that we use that we have almost forgotten that it is a code.

234 actually means 2 x 10^2 + 3 X 10^1 + 4 X 10^0. These powers of 10 are not shown, They are just assumed to be these but hidden from our view.

This clarification would also help students become familiar with decimal representation.

23.4 is just 2 x 10^1 + 3 x 10^1 + 4 x 10^-1 ( or 4/10).

We also think that this representation is "natural". We do not realise that it has become natural because we have got completely used to it.

We can think of two hundred and thirty four as a quantity of toffees made of twenty dozen less six!

In the decimal place value system is written as 234 which means 2 hundreds 3 tens & 4 ones.

This is equivalent to paying this amount with 2 hundred rupees, 3 ten rupees & 4 one rupee notes.

But in real life there are many other way of paying this amount.

In 20 ten rupees & 34 one rupee notes.

Or 234 one rupee notes.

These can also be represented with the place value concept.

We can call these non-standard representations.

The same number can be expressed in different ways using non-standard representation of the place value system, as per the example given below.

Six different ways of representing 34981 - Thirty Four Thousand Nine Hundred Eighty One