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Are you confused when you see numbers with decimals? This post can help you understand decimals. Let’s start by defining what a decimal is. A decimal is really a fraction, with a denominator being implicit to be 10 or some other power of 10. Consider the following decimal examples:

- .6
- .78
- .987
- .1234

What is the denominator in each of these decimal numbers? As mentioned, earlier denominator is implicit or understood from the decimal number. To figure out the denominator, simply count number of digits (or "places") after the decimal point. So for the first decimal number, we have the denominator as 10 because there is only 1 digit after the decimal point. For the second number, we have the denominator as 100 because there are 2 digits after the decimal point. See the following table for summary:

Decimal number | Number of digits after the decimal point | Denominator is | Implicit fraction |
---|---|---|---|

.6 | 1 | 10 | 6/10 |

.78 | 2 | 100 | 78/100 |

.987 | 3 | 1,000 | 987/1000 |

.1234 | 4 | 10,000 | 1234/10000 |

This table can help figure out the right denominator for most of the decimal points:

Number of digits after the decimal point | Denominator is |
---|---|

1 | 10 |

2 | 100 |

3 | 1,000 |

4 | 10,000 |

5 | 100,000 |

6 | 1,000,000 |

7 | 10,000,000 |

Do you see a pattern here? The pattern is that the number of digits you count after a decimal point is the number of 0s you will use as the denominator! As noted earlier, 1 digits means power of 10, 2 digits mean power of 100, and so on.

You may be using decimal calculations everyday even if you don’t realize. For instance, when you purchase something from a store, it is rare to find an item that is evenly price, it is usually like $.99, $1.39, $2.49, $9.99, $49.87, and so on. Don’t forget the tax! It is in decimals, too! For the price of an item, we use two digits after the decimal point, so the denominator is 100. For the tax, for a tax rate of 6% or .06 in Maryland, the denominator is also 100. You don’t want the denominator to be 10, for instance, for tax because you will be paying 60% in taxes instead of just 6%!

The most common uses for decimal numbers is probably adding (such as adding cost of items you want to purchase or sell), or rounding. (You can also do other mathematical operations on decimals such as subtraction, division, etc.)

Rounding decimals simply require locating the decimal place and knowing to what level (i.e., nearest 10^{th}, 100^{th}, or 1,000^{th}?) you want to round to?

If you want to round the following to the nearest 10th,

- .514
- 54.29
- 4545.5879

They will become:

- .5
- 54.3
- 4545.6

If you want to round the same decimals to the nearest 100th,

- .514
- 54.29
- 4545.5879

They will become:

- .51
- 54.29
- 4545.59

Posted on 7/29/2006

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