*hundreds*,

*tens*and

*units*in a number, depending on its place:

## Dictionary Definition

The Oxford English Dictionary defines place value as "the numerical value that a digit has by virtue of its position in a number."## Understanding Place Value

It is easier to understand place value with an example. Consider the number**242.35**. It is made up of the digits 2, 4, 3 and 5. The different digits have different place values, called

*hundreds*,

*tens*,

*units*,

*tenths*and

*hundredths*.

- The
**2**is in the**hundreds**column. It has a value of 200. - The
**4**is in the**tens**column. It has a value of 40. - The
**2**is in the**units**column. It has a value of 2. - The
**3**is in the**tenths**column. It has a value of 3/10ths. - The
**5**is in the**hundredths**column. It has a value of 5/100ths.

**2**appears twice in the number, but has a different value depending on what place it is in.

## Comparing the Magnitudes of Different Place Values

The place values have different magnitudes (sizes). Consider the number**111**. It has a digit of 1 in the

*hundreds*,

*tens*and

*units*places.

**Each place value is 10 times larger than that to its right.**

- A
*ten*is**10 times larger**than a*unit*. The 1 in the*tens*column has a value of 10. This is 10 times larger than the value of the 1 in the*units*column, which is 1. - A
*hundred*is**10 times larger**than a*ten*. The 1 in the*hundreds*column has a value of 100. This is 10 times larger than the value of the 1 in the*tens*column, which is 10.

**Each place value is 10 times smaller than that to its left.**

- A
*ten*is**10 times smaller**than a*hundred*. The 1 in the*tens*column has a value of 10. This is 10 times smaller than the value of the 1 in the*hundreds*column, which is 100. - A
*unit*is**10 times smaller**than a*ten*. The 1 in the*units*column has a value of 1. This is 10 times smaller than the value of the 1 in the*tens*column, which is 10.

## Why Do We Use Place Value

There are an infinite number of numbers. Imagine having to invent a new symbol for every number out there. It would be impossible to invent or remember.To get around this problem, we have invented a decimal number system, which uses 10 digits.But does that mean we can only have 10 numbers? No. By putting the digits in a different position, or place, within a number we can write an infinite number of numbers.## You might also like...

numbersunderstanding the order of operationsunderstanding long additionunderstanding long subtraction

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