A place value is the position of a digit in the written representation of a number. Place values are counted from right to left, starting with the lowest.
The lowest place value is units, the next is tens, then hundreds, thousands, and so on. Every three place values form a class.
Main place values in ascending order:
Any number can be represented as a sum of place-value terms. For example:
5742 = 5000 + 700 + 40 + 2 = 5 · 1000 + 7 · 100 + 4 · 10 + 2.
Such a representation is called the place-value composition of a number. It helps to understand the value of each digit in the notation.
Place-value composition of multi-digit numbers:
A place value is one position in the notation of a number (units, tens, hundreds). A class is a group of three place values (class of units, class of thousands, class of millions). So a class includes three place values.
The number of place values equals the number of digits in the notation of the number. For example, in the number 1234 there are four place values: units, tens, hundreds, thousands.
Place-value terms are numbers corresponding to each place value. For example, for the number 5742, the place-value terms are: 5000, 700, 40, 2. Their sum equals the original number.
Knowledge of place values is needed for correct writing and reading of multi-digit numbers, for performing arithmetic operations place by place (column addition, subtraction, multiplication), for rounding numbers, and for understanding the positional numeral system.
