## Thursday, April 12, 2012

### The Value of a Place

I can remember being told, as a student in primary school, to put a comma every three numbers when writing large numbers. I was told it would separate the hundreds, thousands, millions etc. I remember dutifully doing this with absolutely no sense of why or feeling any nearer to being able to read very large numbers.

Today, we still use the commas when writing large numbers but
unlike the instruction of the last century, we now teach why we put a comma every three numbers. It certainly does separate things but, more importantly, it shows the repetition of the ones, tens and hundreds every three numbers. First we have ones, tens and hundreds of ones, then we have ones, tens and hundreds of thousands and then we have ones, tens, and  hundreds of millions, and so on. If we learn this repetition of the place value referents it makes reading and understanding large numbers much easier.

It also helps students develop a far more realistic idea of what zero, or nought, is.  I remember learning 0 as a "place holder", a bit like a pot holder, perhaps. What did that really mean? The 0 holds a place when there is no number there, perhaps. What nonsense!  The 0 means there are none of that particular referent in this number as in 23,405, where the 0 means there are 0 tens. In this number, 305, 877  the 0 means there are no ten-thousands; there are 3 hundred-thousands and 5 thousands but 0 ten-thousands.

'Nought', by the way is the British word for zero and became quite popular during the first decade  of the current  century with years like '03 and '06 which was referred to as the 'noughties'.