Zero & Place Value System

< 6.7 Understanding Zero 2 | Topic Index | 6.9 Visualizing Place Value 1 >

Zero as a Place Holder

The idea of 0 was first invented as a place holder and is intimately related to the place value system.

The use of 0 in a special way will become apparent if we try to write a number like Four Thousand Three Hundred Five using numerals. There are no Tens used in this number, which also means that this amount in rupees can be paid out without using Ten Rupee notes. If it is written as 435, then it may be read as Four Hundred and Five.

Sumerians used a place value system which could cause confusions. Sumerians used to write this number as 43 5, with a blank in the ten&rsquo;s place. This could cause confusion as the blank may not be clearly discernible while deciphering someone else&rsquo;s written text. The genius of the Hindus was in writing a 0 in the blank space so that there is no confusion.

In the Indian system the above number is written as 4305 which inserts a 0 in the Ten&rsquo;s place, indicating that there is no numeral from 1 to 9, in the Ten&rsquo;s place. Here 0 is used to ensure that the place values of the other numerals are understood clearly. This role of 0 is called a &ldquo;place holder&rdquo;, much like a person reserves a seat in the bus by dropping his handkerchief while standing outside the bus.

Since they also recognised 0 as a number with no countable value, the introduction of 0 in a number does not change its value.

The use of 0, helps us to represent the difference between 205, 502, 250 and 520 in a manner which can be grasped easily by children.

Zero As a Number

We also saw that 0 was also treated as a number. Hence there are now ten numerals for numbers from 0 to 9. Hence the place value system is also called the Decimal Place Value System, Deci being the adjective of ten.

The concept of 0 as a place holder is a much earlier idea than its acceptance as a number.

Inventing a Numeral to Represent Zero

Though it is generally accepted that the place value system originated in India, there was no conclusive scientific proof that the currently used numeral shape of zero (i.e 0) evolved in India.

It was known that in a document called the Bakhshali manuscript lodged in the Oxford University, a dot was used to represent zero. The manuscript was found in a village near Bakhshali in present day Pakistan. It was also accepted that the shape of the present numeral zero (i.e 0) evolved from that dot. But the date of the manuscript had not been established. It was dated anywhere between 200 and 1200 A.D.

Recently the date of the manuscript has been fixed around 300 A.D by carbon dating. So, it can now be conclusively said that the present shape of numeral zero also evolved in India.

How does 0 affect a number?

We saw the necessity of using 0 in a number (between other numerals) just to clarify its correct value. Let us now see the effect 0 will have at the two ends of any number.


 * 1) If 0 is added to the right end of a number it will be the effect of increasing the value tenfold, i.e multiplying it by 10! 45 becomes 450 which is ten times 45.
 * 2) If 0 is added to the left end of a number, its value does not change at all. This is because the place value of the rest of the numerals remains unchanged and the value of 0 still remains 0.   45 is same as 045. 0 is in the hundred's place and its value is 0.
 * 3) Many times, in government forms, 8 spaces are given to write your date of birth and in any government form every space is to be filled.
 * 4) If your date of birth is 6thApril 1960, you have to fill the form as 06 04 1960, writing 6 as "06" and 4 as "04"

But while learning decimal numbers, we will see that these rules need to be modified as the conceptual understanding behind decimal representation is slightly different

< 6.7 Understanding Zero 2 | Topic Index | 6.9 Visualizing Place Value 1 >