Lesson 2
Place Values

The whole-number system consists of only ten different digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Although there are only ten digits, we can combine any number of them to count from zero to infinity ( 0 to ¥ ). In order to create so many combinations of numbers, it is necessary to agree upon some carefully crafted rules.

Topic 1
Digits and Place Values

The rules for creating an infinite number of values out of ten simple digits are based upon the idea of place values—the value of a digit depends upon its place in a series of digits.

Consider the number 384. Reading from right to left (), you can see that there is a 4 in the ones place, an 8 in the tens place, and a 3 in the hundreds place. So the value of this number is three-hundred eighty four:

3 times a hundred
8 times ten
4 times one

What comes after the hundreds place? The thousands place. And after that? The ten-thousands place, the hundred-thousands place, and the millions place. The following table shows the place values up to a billion. This is far enough to account for whole numbers ranging from 0 to 9,999,999,999. We could keep going a lot farther than a billion, but this is far enough for the work in this course.

Place values for whole numbers, ones through billions

Place Range of Values
Ones 1 to 9
Tens 10 to 99
Hundreds 100 to 999
Thousands 1,000 to 9,999
Ten-Thousands 10,000 to 99,999
Hundred-Thousands 100,000 to 999,999
Millions 1,000,000 to 9,999,999
Ten-Millions 10,000,000 to 99,999,999
Hundred-Millions 100,000,000 to 999,999,999
Billions 1,000,000,000 to 9,999,999,999

Identifying Place Values

Use these interactive examples and exercises to strengthen your understanding and build your skills:


Topic 2
Periods of Numbers

Interpreting the value of very large numbers can be very confusing without dividing the place values into periods of three:


If you are having any trouble understanding the content of this lesson, you will benefit from a more detailed tutorial on the subject.