Number systems and place value was not something which I had thought about or realised to be so complex until now. When I was in school and learning how to count or about place value and systems, I understood it straight away and that was it. I never questioned the mathematics behind it or considered it further. It was never explained to me why we use the number system which we do or why there is units, tens and hundreds, but it was just that we do and that was it, case closed. Therefore, when I realised that this is different around the world, and that there was specific reasoning behind it, it intrigued me and I wanted to look into it further.

Why a base 10 number system?

A base 10 number system is the number system which we use in the UK every day. The base 10 number system is also known as the decimal system and has 10 digits to show all numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, which uses place value and a decimal point to separate. The placing and positioning of the numbers in the system are based on powers of ten which is referring to tens, hundreds, thousands etc. Once you exceed the number 9, you then move onto the next highest position (Russell, 2017).

Before this input, I just presumed that everyone around the world used the same base 10 number system as us and that they would just translate it to fit their spoken language. To me it just makes sense, we have 10 fingers to help us count so we have a 10-base number system? No?

It appears however, that not all societies use a base 10 system. The Arara tribe in the Amazon for example use a two-base system:

1. anane (one)
2. adak (two)
3. adak anane (two, one)
4. adak adak (two, two)
5. adak adak anane (two, two, one)
6. adak adak adak (two, two, two) etc.

This confuses me as I do not understand how you are supposed to count by using the same two numbers which are simply repeated over and over again. How does that work when you are counting numbers as big as 100 or 1000? Then again, I suppose that if you are brought up using this, then it would seem normal, just like the base 10 number system seems normal to us. The Arara tribe may not need to count to excessive numbers and therefore, the base 2 system works best for them.

Another alien number system to me is the base 12 number system which is known as the dozenal base system. At first it felt familiar as they also use the numbers 0-9. However, the number 10 looks similar to an upside down 2 and is called ‘dek’, 11 looks similar to a reversed 3 and is called ‘el’ and then 12 looks identical to our number 10 and is called ‘do’ (Dvorsky, 2013). At first I was sceptical about a base 12 number system as a base 10 system seems so much easier to use. When I approached it with an open mind however, I realised that a base 12 number system makes sense for a multitude of reasons. Items such as eggs are measured in dozens, which is equal to 12, 12 has more factors than 10 and the clock dial is also numbered 1-12.

I have attached a video by Numberphile explaining the way the dozinal base system works and it’s benefits. One point which I found extremely interesting in the video however, was that some cultures still use their hands and fingers to count, a point which I raised earlier. Unlike counting their 10 fingers like we do, they count each individual segment on each of their fingers and their pinky which seems more confusing at first, but also makes sense.

One number system which I found confusing, but which I also found the most interesting is the number system which was most commonly used by farmers in North England to count sheep. This was a base 20 system, meaning that the farmers would count to 20 and then pick up a stone to represent the 20, and start again. I have attached a photo which shows the numbers which the farmers would use in Lincolnshire, Yorkshire, Derbyshire, County Durham and Lancashire. I found this interesting as it is a completely different way of counting, not using numbers as such but rather words. It has been argued that the number system used today in countries such as Spain and France, has been influenced by this system. This is because the word for 10 in North England is mostly either ‘Dix’ or ‘Dick’ which is like 10 in French which is ‘Dix’ and Spanish which is ‘Diez’.

After considering various different number systems, we then had the chance to create our own. However, we had to ensure that the numbers and symbols made sense when it comes to using decimal places and doing mathematical sums such as addition, multiplication, subtraction and division. My group decided to use the theme of flowers for our number system. I have attached a photo of my number sequence.

I feel that this activity really helped me put what we had been looking at in the lecture into context. I need to see things visually to help me fully understand it and this gave me the opportunity to do so. It also helped me to wrap my head around different number systems, a concept which I found something extremely confusing and challenging to begin with.

References

Bellos, A. (2010). Alex’s Adventures in Numberland. London: Bloomsbury.

Russell, D. (2017). What Base 10 Means in Mathematics. [online] ThoughtCo. Available at: https://www.thoughtco.com/definition-of-base-10-2312365 [Accessed 2 Nov. 2017].