The Decimal Number System

Introduction to the Decimal Number System

In the Western world, the decimal number system is mostly what everyone knows about numbers.

Everyone knows it.

Post people just know that.

There are many other number systems, but the society decided to use the decimal number system as the default.

Why? I think the reason is that people have 2 hands (and 2 feet) with 5 fingers on them, and counting from 1 to 10 feels natural.

When you reach 10, you start from scratch to reach 20.

That’s my guess, a pretty solid guess.

The decimal number system was invented by Indians and popularized by the Arabs, and it’s still called Hindu–Arabic number system.

The decimal number system is said to have base 10 because it uses 10 digits, from 0 to 9.

Digits are positional, which means the digit holds a different weight (value) depending on the position.

The 1 digit in the number 10 has a different value than in the number 31, because in 10 it is put in position 2, and in 31 it is put in position 1 (counting from right).

While this might sound obvious because you use this system since you were a child, not every number system works this way.

The roman number system, widely used in Europe since ancient Rome to the late middle ages, was still “base 10” but not positional. To represent 10 you used the letter X, to represent 100 you used C, to represent 1000 you used M.

In roman numerals, the number 243 in the decimal number system can be represented as CCXLIII.

You could not move letters around to change their meaning. Letters with a bigger value are always moved left compared to letters with less value. Except relatively to each letter, to form 4 using IV, for example (but this is another topic, let’s get back to decimal numbers).

Any number in the decimal number system can be de-composed as the sum of other numbers, multiplied by the power of 10 depending on their position. Starting at position 0 from the right.

\[10^0\] equals to 1.

\[10^1\] equals to 10.

\[10^2\] equals to 100, and so on.

In the decimal number system:

5 can be represented as \[5\times10^0\]

42 can be represented as \[4\times10^1 + 2\times10^0\]

254 can be represented as \[2\times10^2 + 5\times10^1 + 4\times10^0\]