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 1Digits 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 2Periods 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. |