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The importance of nothing

The Romans did not have a numeral to represent zero. For thousands of years, zero was not even considered to be a number. There was no use for it. In ancient civilizations, if you didn’t own any sheep, you just said “I don’t have any sheep”. You didn’t say “I have zero sheep”.

We’ve seen that in Roman numerals, one hundred and nine is CIX. Notice that there is no need for a zero, whereas in our place value system we use a zero to represent the fact that we have no tens. For example, 109 means “one hundred, zero tens and nine units”.

Today, Hindu-Arabic numerals, the set of 10 symbols 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 are used throughout the western world to represent numbers in the decimal number system.

The symbols originated in India around the 6th century and were introduced to Europe around eight hundred years ago. This represented a profound break with previous methods of counting and paved the way for the development of algebra.

In our modern ‘place value’ system, each numeral can stand for different numbers depending upon where it is in the number. For example:

481 – the 1 stands for one
418 – the 1 stands for ten
148 – the 1 stands for one hundred

The idea of a place value system was developed before the numeral to represent zero was in common usage. In one system without zeros, dots were places above numerals to indicate its value. For example:

\(8 = 8\)
\(\dot{8} =80\)
\(\ddot{8} =800\)

And so on…

So the number 4032 would be written \(\dddot{4}\dot{3}2\).

As there are no hundreds, we just miss out a number with two dots above it.

Over the next few steps, we’ll cover the basics of how base 10 works and how the place value system helps us to calculate addition and subtraction. We then look at how place value can be represented with standard form (powers of 10), before looking at other number bases.

Teaching resources

You can access a number of teaching resources to support the teaching of place value on the STEM Learning website.

Just a reminder that you will need a free account on the STEM Learning website in order to access these additional resources. Completion of the course is not dependent upon access. If you are not based in the UK, please ensure you register as an international user.

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This article is from the free online course:

Maths Subject Knowledge: Understanding Numbers

National STEM Learning Centre