**Introduction to Decimals**

By Lisa Williams

**How we came by decimals and how place value works.**

A decimal is another way to write a fraction. In $4.25 , $0.25 is part of a dollar. It is 25/100 of a dollar.

In a decimal, the farther right the number the smaller it’s value.

Always remember all decimals can be written as fractions.

Our number system is a base 10 system. I can hear you saying, “Why do I need to know this?”

Well, in a base 10 number system you can always change the place value of the number by one spot by either multiplying or dividing by 10. The place values vary by a factor of 10 meaning you either multiply or divide by 10 to change the numbers place value.

Examples:

One-tenth moves one place to the right to the ones place because you multiplied by 10.

1/10 x 10 = 1

0.1 x 10 = 1

Ten moves one place to the right to the tens place because you multiplied by 10.

10 x 10 = 100

One-tenth moves one place to the left because you divided by 10.

1/10 divided by 10 = 1/10 x 1/10 = 1/100

.1 divided by 10 = .1 x .1 = .01

PLACE VALUE CHART: e.g. number 9605872.145673

Note: The numbers to the left and right of the decimal point are arranged around the ones’ position. This rule is amazingly helpful in converting metric units of measurements. I have a simple stair step chart that makes it soo simple.

CHART 2

Note: Included are the latin prefixes and their meanings. You insert grams, liters, or meters after the prefixes to get common units of metric measurement. As you go up this chart to change place value or to convert from say milligrams to centigrams you multiply by 10. As you go down the chart to convert from say deciliters to centiliters you divide. If you expand it out to look like stairs you are dividing when you go down the stairs and multiplying to go up the stairs.

Try to form a picture in your mind of a brick wall ( my husband is brick mason don’tcha know) The wall itself represents the whole number 1.

But this wall is of course made up of bricks or blocks of varying sizes. If all the bricks were of random varying sizes…

Picture a wall without mortar and various differing bricks. It looks like it could fall any minute…

Now let’s look at a wall whose bricks vary in size equally by a factor of 10. The biggest block being the wall itself.

Picture an empty square as that wall:

. . . . . |

The next smallest block being 1/10th or 0.1 in decimal form.

Picture the same square as above divided into 10 equal parts. One part needs to be shaded some color with caption: 1/10 or 0.1 representing the shaded part.

. | . |

. | . |

. | . |

. | . |

. | 1/10 or 0.1 |

Each of these 1/10 or 0.1 blocks can be broken into 10 pieces each. These pieces are 1/100 of the whole or 0.01.

Picture of same square as above divided into 100 equal parts – ten of the them shaded one color with caption 1/10th or 0.1 and one of them shaded different color with caption 1/100 or 0.01

. | . | . | . | . | . | . | . | . | . |

. | . | . | . | . | . | . | . | . | . |

. | . | . | . | . | . | . | . | . | . |

. | . | . | . | . | . | . | . | . | . |

. | . | . | . | . | . | . | . | . | . |

. | . | . | . | . | . | . | . | . | . |

. | . | . | . | . | . | . | . | . | . |

. | . | . | . | . | . | . | . | . | . |

. | . | . | . | . | . | . | . | . | . |

. | . | . | . | . | . | . | . | . | .01 |

Exercise:

Fill in the place value blanks:

What is the place value of the number 4 in the following problems?

1.) 567.431

2.) 981.042

3.) 453.2

4.) 784.32

Write these fractions as decimals.

5. 6/10

6. 5/100

7. 87/ 1000

8. 6/100

9. 734/1000

Answers:

place value chart from left to right;

5 millions

3 hundred thousands

9 ten thousands

0 thousands

4 hundreds

7 tens

6 ones

2 tenths

8 hundredths

4 thousandths

0 ten thousandths

6 hundred thousandths

1 millionths

1.) tenths

2.) hundredths

3.) hundreds

4.) ones

5.) 0.6

6.) 0.05

7.) 0.087

8.) 0.06

9.) 0.734