It’s an arbitrary thing. We use base ten, meaning we use ten digits, 0 - 9. When we reach 9, we roll over to 1 ten and 0 ones, or 10. Like another user pointed out, this may be a result of our number of fingers. But we could use base twelve. Or eight. Or seven.

So the answer to your question is: because some old dead dudes decided to start, and we kept it going.

That has not always been the case. You might have seen videos mocking French because instead of 97 ("ninety-seven") they say four-twenty-and-seventeen. That's a leftover of a time when people counted in base 20 instead of base 10.

The Georgian language functions the same way. 74 is pronounced as "three-twenty-and-fourteen", 51 as "two-twenty-and-eleven".

Over time though, base ten has "won" as humans tend to count of their fingers and we have ten of those. Counting with your toes can't have been practical

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So the concept you're digging down is known as the "base" of a number system.

Numbers do not need to be denominated with any particular symbols. We choose those kind of arbitrarily. There have been a lot of number systems that have emerged from different cultures over time, and the ones that stand the test of time do so because they are useful and efficient for communicating information. The Babylonians used a sexagesimal (base 6) system, which did all right for a while, but was ultimately replaced (like virtually all number systems of antiquity) by our current base-10 numerical system, courtesy of the Hindu-Arabic tradition.

So what does it mean for something to be base 6 rather than base 10? In our base 10 system, you know that each digit represents one of ten possible values (0 - 9). In base 6 it's the same, just with fewer values (0 - 5). When you roll over to the next digit in base 10, that next digit represents some power of 10 (10, 100, 1000, etc.) When you roll over to the next digit in base 6, the next digit represents some power of 6 (6, 36, 216, etc.). So, to write the value of "ten" in base 10, we write "10" (1 in the 10's digit plus 0 in the 1's digit = ten). To write the value "ten" in base 6, we write "14" (1 in the 6's digit plus 4 in the 1's digit = ten).

So why did base 10 win out against everything else? Well, in the end, it's useful and easy to work with for a human, for a lot of reasons. It's an even number, so we can halve it easily. We have ten fingers usually, so that makes counting in base 10 sort of intuitive. The value also finds a sort of sweet spot where it can be used to efficiently compute and communicate information. The lower in base you go, the fewer values each digit holds, so a number in a lower base will often take more digits to write than the same number in a higher base. That means higher bases can represent values more efficiently (i.e., with fewer digits) and the computation of numbers (which is traditionally done digit-by-digit, if you're doing it by hand) can be done with fewer steps in a higher base as well. Of course, human calculators don't want too high of a base because then we have to have a deeper library of symbols/values for each digit of our numbers. That makes the scheme more difficult/laborious to learn, and the more symbols you add, the more you rely on nuances in those symbols to distinguish them from one another (which isn't ideal if you're dealing with human calculators).

So to circle back and answer your question, 9 is the "last" value because we use base 10, and we use base 10 because it's a great balance of efficient and intuitive, as time has proven.

1, 2, 3, 4, 5, 6, 10? 11, 12, 13, 14, 15, 16, 20?

Are you asking why we don't use base 7 or why we use base 10?

Different number systems have been used through the years for different purposes, see binary and hexadecimal. 10 is just the easiest and most universal.

Because we decided on it. We use a base-10 system with ten digits (0-9), and we prefix digits to indicate powers of ten (so the rightmost digit is the ones, the next one to the left is tens, then hundreds, then thousands etc)

We can do the same with any base. You may have heard that computers and computer programmers often use binary. That's base 2 (where we use the digits 0 and 1, and the rightmost digit is ones, the next is twos, then fours, then eights and so on).

Hexadecimal is also commonly used with computers. That's base-16. So we use the digits 0-9 plus the letters a-f to mean "ten" through "fifteen". So the rightmost digit is, as always, the ones, then we have the sixteens, then the 256's and so on.

The general system works with any number. We've just decided to settle on 10 for our everyday number needs.

We have ten fingers. This simple convenience overtook other methods of counting (by twenties, etc).

The best explanation I've heard is that we count in sets of ten because we have ten fingers, making the sets of ten easier to understand and visualize.

There is no real reason. Base 10 as the default system probably comes from counting with fingers, but there's no reason we couldn't do math in base-12 if we counted with joints instead.

Ancient Babylonians counted with base-60. We still measure time in increments of 12 and 60 because of that, but also because both 12 and 60 are convenient bases to work with since they're easily divisible by 2, 3, 4 and 6.

I am satisfied already. Thank you to all posting answers. Regards.

It's a cultural thing.
We have 10 fingers, and a lot of people counted that way.
There's another way where you point to a finger bone with a thumb, that way you can count to 12. They mostly lost out to 10, but you still see them all over the place. Most notably the clock. It's 12pm somewhere in the world right now.

Programmers work in powers of 2, and 16 is a convienent power that closely mirrors how we used to set up memory. There are 16 combinations of four 1s/0s in a row and 8 1s/0s in a row make up one computer byte. Hence why you see programmers use numbers like 1F A2 FF

You could count to any number, but these are some of the most common ones.

There is a pretty interesting book called «Zero» that delves in to the history behind how human cultures have been using numbers for counting and calculations. Especially how the introduction of «zero» made big changes in how we count and relate to numbers. The babylonians used 60 as a base, which we still use today when measuring time (seconds and minutes). Apparently there are still some tribes that have names for only three or four numbers (1, 2, 3, 4), because they haven’t had the need for any higher numbers in their everyday lives. One factor for our need for higher numbers comes from our eventual trading in higher volumes and the development of more complex calculations.

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The ancient Greeks likes 12, medieval Europe liked 20, and computers like 2. Any of them are as valid as the others, but as a society we ended up at 10. I would guess having 10 fingers had a lot to do with it.

Although we use base 10 for most counting today, it's worth noting that base 12 shows up in a lot of ways too. It's arguably more optimal, since it allows you to divide cleanly by multiples of 2, 3, and 4, rather than just 2 and 5.

Early numbering systems used base 12, which is why you'll see things like time (60 seconds, 24 hours) or angles (360 degrees) use multiples of it, because easy divisibility is useful for those things.