Decimal Number System

The number system that represents a number in terms of 0 to 9 digits is a decimal number system. A decimal number system has ten digits, i.e., 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The base of a number in this system is 10. In the decimal number system, a number is expressed in terms of powers of 10, i.e., the positions of successive digits to the left of the decimal point represent units, tens, hundreds, thousands, and so on.

Some examples of numbers in the decimal number system are (23)₁₀,(123)₁₀, (5547)₁₀, (6531)₁₀, and so on. In everyday life, we most frequently represent numbers using the decimal number system.

For example, (123)₁₀ in powers of 10 is expressed as 1 × 10² + 2 × 10¹ + 3 × 10⁰. 1 is in the hundreds place, 2 is in the tens place and 3 is in the units place.

Decimal Number is defined by the number which has a whole number and the fractional part separated by a decimal point. While Binary Number is defined by a number which is expressed as in the base-2 numeral system. It is always written in the form of 0 and 1. In math, a system that is used to represent numbers in different forms is called number system.

A mathematical value that is used to count, measure, and perform various arithmetic calculations is called a number. Based on properties, numbers are classified into different types, such as natural numbers, whole numbers, fractions, rational and irrational numbers, and so on.

In a similar way, we have different kinds of number systems based on different properties, such as a binary number system, an octal number system, a decimal number system, and a hexadecimal number system. We can convert a number from any number system into any of the other three number systems.

We have curated the difference between Decimal and Binary Number in detail below.