Place value is a very important concept in mathematics that helps to perform counting and calculations of numbers in a convenient way. A number can have many digits and depending on the position of the digit in the number, each digit is assigned a value which is called place value. It can also be said that the place value indicates the position of each digit in a number. To find the position of a digit, we start counting from the rightmost digit of a number and continue towards the left. The rightmost position is termed as units place or one’s position and further positions from right to left of the number are denoted as tens, hundreds, thousands, and so on. Place value basically describes the value that each digit carries for the number. You may learn more about this topic at Cuemath.

For example, the place value of each digit in the number 5463 can be determined as follows:

Place values of 5 =4 × 1000 = 5000 or 5 thousand

Place value of 4 = 4 X 100 = 400 or 4 hundred

Place value of 6 = 6 × 10 = 60 or 6 tens

Place value of 3 = 3 × 1 = 3 or 3 ones

Using the above concept of the place value of digits in numbers, we can write numbers in their expanded form. For example, the expanded form of the number 15438 is 10,000 + 5,000 + 400 + 30 + 8.

In mathematics, there are two systems of place value commonly in use. These are the Indian place value system and the International place value system. In both cases, the counting starts from the rightmost digit and both systems use groups of digits separated by commas to denote the place value. However, there is a difference in the naming convention of place values between both systems.

In the Indian place value system, the place values are named as ones, tens, hundreds, thousands, ten thousand, hundred thousand, millions, and ten million.

In the International place value system, the place values are denoted as ones, tens, hundreds, thousands, lakhs, ten lakhs, crores, and ten crores.

## What is the Number System?

In a number system, a number is denoted using some digits or characters or a combination of both. The number of digits or symbols used to represent a number determines the base of the number system. Depending on the position, every digit in a number corresponds to a value. The number system is a very important concept that is commonly used in mathematics for performing various calculations.

A number system is characterized by its base value which can be different for different number systems. The base of a number system represents how many different digits are available to denote a number. The most commonly used number system in mathematics is the decimal number system in which a number is expressed using the digits from 0 to 9. In computer data handling, a Binary number system is used consisting of only two digits, 0 and 1. The other two number systems are the Octal number system and the Hexadecimal number system. The octal number system uses eight digits (0 to 7). In the Hexadecimal number system, a number is denoted by a combination of ten digits (0 to 9) and six alphabets (A to F)

It can be said that a number system helps to translate number names into digits. The study of different number systems such as decimal (base 10), binary (base 2), octal (base 8), hexadecimal (base 16) helps to gain a general understanding of how number systems work.

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