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Types of Numbers
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Adding and Subtracting Decimals

To add decimals, remember that decimals are abbreviations for fractions.

0.3 + 0.04 + 0.001 translates to .

Since and , this means that .

Is this paragraph making you dizzy? Well, stop running in circles, sit down, and for goodness' sake, eat something!

The example in the previous paragraph represents the long way to do things. (Sigh of indescribable relief.) While it's mathematically correct to turn decimals into fractions, add the fractions, then turn them back into decimals, it's too much work. Solving decimal problems that way would be like deleting all your songs on iTunes and then uploading them again just so you can change the order of your playlist. By the way, David Hasselhoff Sings America? Really?

Instead, remember that adding zeros to the end of a decimal doesn't change its value, so 0.3 = 0.300. (This is the same as saying  but without having to write the fractions.)

Also, we can rewrite the 0.04 part of the problem as 0.040. The last part, 0.001, is already written out to the thousandths place, so we can leave that one alone. Good thing, because all this decimal manipulation is wiping us out.

To add up the decimals, always add zeros to the ends of the decimals as needed so that all of them have the same number of decimal places (like we did above). Line up the numbers at the decimal point, and add them like whole numbers:

   0.300
   0.040
+ 0.001
= 0.341

We're really adding up  just like we did before, but without having to write the fractions. Good thing, because all this fraction writing is wiping us out. In hindsight, maybe we just didn't get enough sleep last night.

Subtraction is similar. To subtract one decimal number from another, first give the two decimals the same number of decimal places by adding zeros at the end as needed. Line up the numbers at the decimal point, and then carry out the subtraction as you would with whole numbers. If you have a different, "cool" way of subtracting whole numbers, then never mind.

Next Page: Multiplication and Division by Powers of 10
Previous Page: Comparing Decimals

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