# The Decimal System and the Mathematical Place Value

The Decimal System
Another word for the decimal system is the base 10 system. Numbers are grouped by tens in the decimal system, which means that the decimal system, or the base 10 system, only has ten different numerals being used to make u the decimal numbers. The ten numeral are used separate from each other and then afterward they are combined with one another to create even more numbers that are mixtures of the original ten numerals of the decimal system. The ten numerals of the decimal system, or base 10 system, are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

There are alternatives to the decimal system. The binary system, otherwise known as the base 2 system, doesn’t use anymore than two numerals, representing every number from zero to infinity. Those two numerals are 0 and 1. Base 5 is another alternative. Just like in base 2, the numerals in base 5 are combined with one another to represent all numbers from zero to infinity. Base 5 uses five different numerals, which are 0, 1, 2, 3, and 4.

Place Value
If you look at the number 111, it only involves one numeral. The only numeral in the number is 1, which has a different meaning based on its position in the number. The first 1 stands for 100, the second 1 stands for 10, and the last 1 only stands for 1. The fact that this one numeral can stand for multiple numbers is called place value. This means that the numeral’s value is determined by what place it is within the number.

Place value is important because it allows us to only have ten numbers, which is much simpler than if we had to use an entirely different number for every number in existence. When a number consists of multiple numerals, the value of each numeral is ten times greater than the numeral that sits on its right side.

If a number has more than three numerals, then the numerals need to be separated by a comma, or multiple commas, depending on the amount of numerals. Counting from the right, a comma must be placed after every group of three numerals.

Zero is used as a place holder. If there is 0 after 1, then that means there are 10 ones. If there are two zeroes after a 1, then that means there are 100 ones and so on and so forth.

Share.