Why do we use a base 10 number system?

Easy peasy question many people might think. We have ten fingers so it can be a tool to help us count. However, how many teachers told you as a child to not use your fingers to count? I remember hiding my fingers under the table from around primary five upwards to count.

What about topics that we use in maths that don’t use a base ten system? Time. Time uses a base 60 for minutes and seconds. Time uses a base twelve system for the hours. Why don’t we count in any of these base systems? This is why time can be very difficult for a child to learn. When counting they have only ever used a base ten system and then when we introduce time anything familiar goes out the window. They are now introduced to counting in 60’s for each minute, for each hour. Another student on this elective discussed whether or not we should still be teaching time because of this (Dunne, 2015) – her opinion gives for an interesting read.

So apart from having our fingers as a tool I thought I would have a look into other base systems and the advantages of using a base ten system in this post.

As already discussed briefly in a previous post (“Our Number System”) there have been numerous different number systems which count in different base systems. The Sumerians “developed the earliest known number system” which had a base 60 system. The base 60 numeral system came from two tribes merging together as one used a base 12 numeral system and the other used a base 5 system and the lowest common multiple of both systems would be 60. Their symbols for their number system are below:

A base 60 system would perhaps make teaching time a lot simpler than a base 10 system. It would make sense for the minutes and the seconds but would also be very confusing still for the hours. On the other hand, this system has a lot of symbols which could be quite challenging for children to learn.

However, a base ten system does have a number of benefits. The base 10 system allows for simple explanations of hundred tens and units etc. Using a base two system such as the Arara tribe in the Amazon would get very repetitive and confusing rather quickly but on the other hand using a base 60 system it would take a long time until you exchange it for another to start again. A base 10 system has the benefit that it is big enough to not be repetitive but small enough that you are not continuously counting before exchanging.

This has given me a profound understanding of why our base system has come about. The benefits of the base ten system and why this is simple, as well as complicated when it comes to things like time or angles, for children to learn to count. Although there are many different types of number systems that are not just out normal base ten system or the roman numeral system that we teach children which I could use to broaden children’s knowledge, in my future career, on the different types of number systems such as showing them the yan, tan, tethera… video below as a different type of number system (a base 20 system) used for counting sheep more commonly used in the early 20^th century but still used by farmers now.

References:

Dunne, J. (2015) Is it time to scrap time? Available at: https://blogs.glowscotland.org.uk/glowblogs/jennysjourney/2015/10/25/is-it-time-to-scrap-time/ (Accessed: 4/11/15)