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:

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.
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.