The Lesson
Place value tells us the value of a digit depending on what place it is in a number.
Place value means the digits tell us the number of
hundreds,
tens and
units in a number, depending on its place:
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.
Notice that the digit
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.
Lesson Slides
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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.