Decimal Number System

The decimal number system is the standard system for denoting integer and non-integer numbers.

What is the decimal number system?

Long ago, humans created a number system that has exactly ten digits.

This number system is called the Decimal Number System and the digits in this number system are 0 1 2 3 4 5 6 7 8 9.

If a number system has n digits, we say that the base of the number system is n. So, the decimal number system can also be called a base-10 number system.

Let’s look at place values for decimals in the below picture.

Place Value for Decimals
Place Value for Decimals

We write the number in one row and multiple columns. The rightmost column corresponding to the rightmost digit is called the one’s place. The second right column is called the tens place, and we go on increasing in multiples of tens, e.g., hundreds place, thousands place, and so on.

Suppose we have to represent this in powers of 10. In that case, the rightmost place (or the least significant digit) corresponds to 10010^{0} and continues 10110^{1} and so on towards the left side.

Decimal Number System Example

Let’s write the number 1256 in the decimal number system.

int n = 1256;

Repeatedly do the modulo operation until n becomes 0 using:

%” and “division” operations.

n (value) n n/10 (Quotient) n%10 (Remainder)
n is 1256 1256 125 6
n/10 becomes 125 125 12 5
n/10 becomes 12 12 1 2
n/10 becomes 1 1 0 1

Let’s visualize this below: