A numeral system is a writing system for expressing numbers, using digits or other symbols in a consistent manner. Here in the United Kingdom we use a simple base 10 system or decimal number system. In base 10, each digit in a position of a number can have an integer value ranging from 0 to 9 (10 possibilities). The places or positions of the numbers are based on powers of ten (e.g., hundredths, tenths, tens, hundreds, thousands). Exceeding the number 9 in a position starts counting in the next highest position. This seems simple to those who have been brought up using the base 10 system, but is it the only system we use?

Lets start with the most relatable, a base 60 system that is used all around the world every single second of every day. TIME! We use this base 60 system everyday, with both seconds and minutes using the numeral system. The base 60 system counts up from zero all the way to 59 before changing into another set, for example; if we had 57 seconds on a timer, but there was 6 seconds to be added, we would say that it took 1 minute 3 seconds, and not 63 seconds. The use of a base 60 system is actually older than that of the base 10 system. The ancient Sumerians, the oldest known civilization on Earth (c4500–c1700 B.C.) used a sexagesimal system too that can still be seen today, in angles, bearing and most importantly time. But why are base systems so important?

The use of a base system makes it easier to count large numbers, using the example of the seconds can show this perfectly. There are 86400 seconds in one day, but this is a mouthful and would be hard to keep track of throughout the day, using the base 60 system of seconds we can reduce this down to 1440 minutes in a day, making it much easier to work with. But wait, Minutes too use a base 60 system so we can reduce the 1440 minutes even further to 24 hours, thus creating time as we know it today in the 24 hour clock. Other number systems can include a dozenal system (base 12), Binary (base 2) and many many more. Base systems, put simply, are just ways of communicating numbers in the simplest form necessary for what you are trying to count.

Richard HolmeHello Max. I liked reading this and illustrating the base 60 systems with time was interesting. Could you also link this to the idea of division and even the principle of equivalence? Aslo can you link this to the ideas within PUFM? Anyway thanks for posting. I look forward to seeing what is next!

MooneyGreat post, Max. You have included a lot of in depth information on this area and have shown you have a good understanding. Do you have any thoughts about how you may use this knowledge in the future and when you are teaching? Overall, a very informative post that has developed my own knowledge on this subject.

Jodie ColvinI agree very interesting post! looking forward to reading more from you Max