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.
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.
- 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.