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Introduction to Decimals
By Lisa
Williams
January
24, 2002
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:
Ten moves one place to
the right to the tens place because you multiplied by 10.
Onetenth moves one place
to the left because you divided by 10.
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...
... the wall would not only look a mess but without mortar would surely fall on you. 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.
The next smallest block
being 1/10th or 0.1 in decimal form.
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
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:
1.) tenths

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