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Concept

# Place Value

Each digit in a number can have a different value, depending on where it is placed – even if it is the same digit. Consider writing the amount of $11$ dollars.

Even though both of the ones in this number are the same digit, they are different because of their place value. The left one is in the tens place and the right one is in the ones place. Place value can be used to write numbers in expanded form. $\begin{gathered} \11.00\ \ =\ \ \10\times 1\ \ +\ \ \1\times 1 \end{gathered}$ For a number written in expanded form, each digit is multiplied by its corresponding place value before being added together. In the case of cash, the expanded form can represent different denominations of money, one $\10$ bill and one $\1$ bill being added together makes $\11.$ Here is another example with numbers.

By breaking this number down into its individual digits and place values, the importance of place value in numbers can be demonstrated.

Digit Place Value Value
$4$ Ten-thousands $40\,000$
$7$ Thousands $7\,000$
$2$ Hundreds $200$
$9$ Tens $90$
$7$ Ones $1$
$1$ Tenths $0.1$
$5$ Hundredths $0.05$
$8$ Thousandths $0.008$