Place Value

We use a base-10 number system which means that each digit in a number is worth ten times the digit to its right. 

When dealing with whole numbers, the number farthest to the right is the ones digit. That place value tells how many wholes (less than 10) are in the number.

Take the number:

1, 234, 567, 890

In this number, there are:

0 ones

9 tens

8 hundreds

7 thousands

6 ten-thousands

5 hundred-thousands

4 millions

3 ten millions

2 hundred millions

1 billion

The place values of each digit are based upon this "multiply the prior digit by 10" process.  The chart below shows the same number and names the "place value" of each digit or column. 

$$\eqalign{ & \large{\mathbf{1,}}\;\;\;\;\;\;\;&& \large{\mathbf{2}}\;\;\;\;\;\;&&& \large{\mathbf{3}}\;\;\;\;\;&&&& \large{\mathbf{4,}}\;\;\;\;&&&&& \large{\mathbf{5}}\;\;\;\;&&&&&& \large{\mathbf{6}}\;\;\;&&&&&&& \large{\mathbf{7,}}\;\;&&&&&&&& \large{\mathbf{8}}\;&&&&&&&&& \large{\mathbf{9}}&&&&&&&&&& \large{\mathbf{0}}\\\\ &\text{B}&&\text{H}&&&\text{T}&&&&\text{M}&&&&&\text{H}&&&&&&\text{T}&&&&&&&\text{T}&&&&&&&&\text{H}&&&&&&&&&\text{T}&&&&&&&&&&\text{O}\\ &\text{i}&&\text{u}&&&\text{e}&&&&\text{i}&&&&&\text{u}&&&&&&\text{e}&&&&&&&\text{h}&&&&&&&&\text{u}&&&&&&&&&\text{e}&&&&&&&&&&\text{n}\\ &\text{l}&&\text{n}&&&\text{n}&&&&\text{l}&&&&&\text{n}&&&&&&\text{n}&&&&&&&\text{o}&&&&&&&&\text{n}&&&&&&&&&\text{n}&&&&&&&&&&\text{e}\\ &\text{l}&&\text{d}&&& &&&&\text{l}&&&&&\text{d}&&&&&& &&&&&&&\text{u}&&&&&&&&\text{d}&&&&&&&&&\text{s}&&&&&&&&&&\text{s}\\ &\text{i}&&\text{r}&&&\text{M}&&&&\text{i}&&&&&\text{r}&&&&&&\text{T}&&&&&&&\text{s}&&&&&&&&\text{r}&&&&&&&&& &&&&&&&&&& \\ &\text{o}&&\text{e}&&&\text{i}&&&&\text{o}&&&&&\text{e}&&&&&&\text{h}&&&&&&&\text{a}&&&&&&&&\text{e}&&&&&&&&& &&&&&&&&&& \\ &\text{n}&&\text{d}&&&\text{l}&&&&\text{n}&&&&&\text{d}&&&&&&\text{o}&&&&&&&\text{n}&&&&&&&&\text{d}&&&&&&&&& &&&&&&&&&& \\ &\text{s}&& &&&\text{l}&&&&\text{s}&&&&& &&&&&&\text{u}&&&&&&&\text{s}&&&&&&&&\text{s}&&&&&&&&& &&&&&&&&&& \\ & &&\text{M}&&&\text{i}&&&& &&&&&\text{T}&&&&&&\text{s}&&&&&&&\text{s} &&&&&&&& &&&&&&&&& &&&&&&&&&& \\ & &&\text{i}&&&\text{o}&&&& &&&&&\text{h}&&&&&&\text{a}&&&&&&& &&&&&&&& &&&&&&&&& &&&&&&&&&& \\ & &&\text{l}&&&\text{n}&&&& &&&&&\text{o}&&&&&&\text{n}&&&&&&& &&&&&&&& &&&&&&&&& &&&&&&&&&& \\ & &&\text{l}&&&\text{s}&&&& &&&&&\text{u}&&&&&&\text{d}&&&&&&& &&&&&&&& &&&&&&&&& &&&&&&&&&& \\ & &&\text{i}&&& &&&& &&&&&\text{s}&&&&&&\text{s}&&&&&&& &&&&&&&& &&&&&&&&& &&&&&&&&&& \\ & &&\text{o}&&& &&&& &&&&&\text{a}&&&&&& &&&&&&& &&&&&&&& &&&&&&&&& &&&&&&&&&& \\ & &&\text{n}&&& &&&& &&&&&\text{n}&&&&&& &&&&&&& &&&&&&&& &&&&&&&&& &&&&&&&&&& \\ & &&\text{s}&&& &&&& &&&&&\text{d}&&&&&& &&&&&&& &&&&&&&& &&&&&&&&& &&&&&&&&&& \\ & && &&& &&&& &&&&&\text{s}&&&&&& &&&&&&& &&&&&&&& &&&&&&&&& &&&&&&&&&& \\}$$

The pattern to the left continues, each set of three numbers has a base value (ones, thousands, millions, billions, trillions, etc).  The next digit is a "tens" version of that base value (tens, ten thousands, ten millions, etc.) and the third number in the set is the "hundreds" value of that set (hundred, hundred thousands, hundred millions, etc.).

The sets go on to infinity but the first 10 are:

When students need to learn place value, they need to memorize (at least the first few of) the place values listed above.  Then, when asked the value of a particular place in a number, they should be able to look at any number, find the digit in that place, and say what that digit is worth (state the digit bfore the the place value: 4 thousand).

Example:

In the number 14,567, what is the value of the thousands place?

The digit in the thousands place is 4; it is worth 4 thousand.

Kindergarteners typically learn one and tens place value.

First graders learn through the hundreds place.

Second graders tend to learn how the numbers go up through infinity.  Most people do not memorize the names past trillion, but they do know how the pattern works (so if they learn the bases above, they can extrapolate from there).