Quick, which number is bigger: 1489012 or 54? It’s 1489012, but how can you tell? It has more digits so it has to be larger, but why exactly is that the case?
Our number system was developed by 8th century Arabic mathematicians and was successful because it made arithmetic operations more sensible and larger numbers easier to write and comprehend.
The breakthrough those mathematicians made required defining a set of rules for how to depict every number. First we decide on an alphabet: different glyphs, or digits, that we’ll use to write our numbers with. The alphabet that we use to depict numbers in this system are the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We call the length of this alphabet our radix (or base). So for our decimal system, we have a radix of 10.
Next we need to understand what those digits mean in different positions. In our system we have a ones place, a tens place, a hundreds place and so on. So what do digits mean in each of those places?
This is where explaining gets a little complicated because the actual knowledge might feel very fundamental. There’s a difference, for instance, between the digit ‘6’ and the actual number six that we represent with the digit ‘6’. This difference is similar to the difference between the letter ‘a’ (which we can use in lots of words) and the word ‘a’.
But the core of the idea is that we use these digits to represent different values when they’re used in different positions. The digit 6 in the number 26 represents the value 6, but the digit 6 used in the number 86452 represents the value 6000.
What changes when a number is used in different positions? How much bigger or smaller does it get?